Higher Topos Theory

Abstract

This purpose of this book is twofold: to provide a general introduction to higher category theory (using the formalism of "quasicategories" or "weak Kan complexes"), and to apply this theory to the study of higher versions of Grothendieck topoi. A few applications to classical topology are included.

735 pages. An updated and expanded version of the earlier submission math.CT/0306109 2/10/07: Various minor additions and corrections; added some material on combinatorial model categories to the appendix. 3/8/7: Actually uploaded the update this time; added material on fiber products of higher topoi. 7/31/08: Several sections added, others rewritten

References in corpus (2)

• Simplicial structures on model categories and functors
• On non-strict notions of $n$-category and $n$-groupoid via multisimplicial sets

Cited by in corpus (519)

• Covariantly functorial wrapped Floer theory on Liouville sectors
• The six operations in equivariant motivic homotopy theory
• Twisted differential String and Fivebrane structures
• Enriched $\infty$-categories via non-symmetric $\infty$-operads
• From algebraic cobordism to motivic cohomology
• Nilpotence and descent in equivariant stable homotopy theory
• Dendroidal sets and simplicial operads
• On the Classification of Topological Field Theories
• Dendroidal sets as models for homotopy operads
• Integrating quantum groups over surfaces
• On the algebraic K-theory of higher categories
• Differential cohomology in a cohesive infinity-topos
• Universality of multiplicative infinite loop space machines
• Principal infinity-bundles -- General theory
• Loop Spaces and Connections
• Model Structures on Commutative Monoids in General Model Categories
• A quadratic refinement of the Grothendieck-Lefschetz-Verdier trace formula
• Algebraic weak factorisation systems I: accessible AWFS
• Decomposition spaces, incidence algebras and Möbius inversion I: basic theory
• (Op)lax natural transformations, twisted quantum field theories, and "even higher" Morita categories
• On the Unicity of the Homotopy Theory of Higher Categories
• The Character Theory of a Complex Group
• Units of ring spectra, orientations, and Thom spectra via rigid infinite loop space theory
• The Picard group of topological modular forms via descent theory
• Parametrized spectra, multiplicative Thom spectra, and the twisted Umkehr map
• On exact infinity-categories and the Theorem of the Heart
• Derived Algebraic Geometry V: Structured Spaces
• Motivic and Real Etale Stable Homotopy Theory
• Relative Calabi-Yau structures
• Brauer groups and étale cohomology in derived algebraic geometry
• Admissibility and rectification of colored symmetric operads
• Wrapped microlocal sheaves on pairs of pants
• A higher stacky perspective on Chern-Simons theory
• Extended higher cup-product Chern-Simons theories
• On the homotopy theory of enriched categories
• Units of ring spectra and Thom spectra
• Microlocal Morse theory of wrapped Fukaya categories
• Boundary-bulk relation for topological orders as the functor mapping higher categories to their centers
• Models of G-spectra as presheaves of spectra
• Pre-Lie deformation theory
• Enhanced six operations and base change theorem for higher Artin stacks
• Presentably symmetric monoidal infinity-categories are represented by symmetric monoidal model categories
• Two-dimensional categorified Hall algebras
• Loop group actions on categories and Whittaker invariants
• Geometrization of the local Langlands correspondence
• Derived Galois deformation rings
• Rigidification of quasi-categories
• The nonequivariant coherent-constructible correspondence for toric stacks
• On 2-form gauge models of topological phases
• Principal infinity-bundles - Presentations
• Algebraic weak factorisation systems II: categories of weak maps
• Decomposition spaces, incidence algebras and Möbius inversion II: completeness, length filtration, and finiteness
• Local duality in algebra and topology
• Mirror symmetry for very affine hypersurfaces
• Genuine equivariant operads
• Non-Archimedean analytic geometry as relative algebraic geometry
• Enhancing the filtered derived category
• Differential Graded Categories are k-linear Stable Infinity Categories
• Comparing composites of left and right derived functors
• On (Enriched) Left Bousfield Localization of Model Categories
• Smoothness of equivariant derived categories
• Categorical notions of fibration
• Completed power operations for Morava E-theory
• Internal categories, anafunctors and localisations
• On the combinatorics of exact Lagrangian surfaces
• Sheaves of categories and the notion of 1-affineness
• A stable infinity-category of Lagrangian cobordisms
• Stable Infinity Categories
• On the homotopy groups of spheres in homotopy type theory
• Definability and approximations in triangulated categories
• On algebraic spaces with an action of G_m
• Exact completions and small sheaves
• Decomposition spaces, incidence algebras and Möbius inversion III: the decomposition space of Möbius intervals
• C_2-equivariant stable homotopy from real motivic stable homotopy
• Simplicial structures in higher Auslander-Reiten theory
• Topological Hochschild homology and integral $p$-adic Hodge theory
• Topological Fukaya category and mirror symmetry for punctured surfaces
• The Enriched Grothendieck Construction
• Lifting homotopy T-algebra maps to strict maps
• Parametrized higher category theory
• M/F-Theory as Mf-Theory
• $t$-Structures on stable derivators and Grothendieck hearts
• Homotopical resolutions associated to deformable adjunctions
• Coherent sheaves on the stack of Langlands parameters
• The stack of Yang-Mills fields on Lorentzian manifolds
• Cdh descent in equivariant homotopy K-theory
• Fukaya Categories as Categorical Morse Homology
• Type theory and homotopy
• The intersection motive of the moduli stack of shtukas
• Sets in homotopy type theory
• Differential graded Lie algebras controlling infinitesimal deformations of coherent sheaves
• K-theory and topological cyclic homology of henselian pairs
• Homotopy Theoretic Models of Type Theory
• Compact generation of the category of D-modules on the stack of G-bundles on a curve
• Ramond-Ramond fields and twisted differential K-theory
• The homotopy theory of type theories
• Smooth 2-Group Extensions and Symmetries of Bundle Gerbes
• Operads of genus zero curves and the Grothendieck-Teichmüller group
• Algebras over infinity-operads
• Shifted Symplectic Structures
• Abstract representation theory of Dynkin quivers of type A
• Differential cohomotopy versus differential cohomology for M-theory and differential lifts of Postnikov towers
• Linear Yang-Mills theory as a homotopy AQFT
• Twisted differential cohomology
• Zero-pointed manifolds
• Geometric Cobordism Categories
• The Atiyah-Bott formula for the cohomology of the moduli space of bundles on a curve
• Brauer groups and Galois cohomology of commutative ring spectra
• Univalence in locally cartesian closed infinity-categories
• Calabi-Yau structures on topological Fukaya categories
• D-manifolds, d-orbifolds and derived differential geometry: a detailed summary
• Virtual fundamental classes of derived stacks I
• Kan replacement of simplicial manifolds
• Enriched model categories and presheaf categories
• A graphical category for higher modular operads
• Higher Hochschild cohomology, Brane topology and centralizers of $E_n$-algebra maps
• Noncommutative Motives I: A Universal Characterization of the Motivic Stable Homotopy Theory of Schemes
• Models of Type Theory with Strict Equality
• A general context for Goodwillie Calculus
• Simplicial nerve of an A-infinity category
• Tilting theory for trees via stable homotopy theory
• Derived, coderived, and contraderived categories of locally presentable abelian categories
• Weak model categories in classical and constructive mathematics
• Homotopy Coherent Mapping Class Group Actions and Excision for Hochschild Complexes of Modular Categories
• Derived Algebraic Geometry IV: Deformation Theory
• Kato-Nakayama spaces, infinite root stacks, and the profinite homotopy type of log schemes
• The Morel-Voevodsky localization theorem in spectral algebraic geometry
• Local duality for structured ring spectra
• Quantization via Linear homotopy types
• All about the Grothendieck construction
• Primary operations in differential cohomology
• A Theory of Elementary Higher Toposes
• Fibration Categories are Fibrant Relative Categories
• A K-theoretic approach to Artin maps
• Sheaf quantization in Weinstein symplectic manifolds
• External triangulation of the homotopy category of exact quasi-category
• The abstract cotangent complex and Quillen cohomology of enriched categories
• On the extended Whittaker category
• Massey products in differential cohomology via stacks
• Parametrized spaces model locally constant homotopy sheaves
• Simplicial principal bundles in parametrized spaces
• Flat vs. filtered colimits in the enriched context
• K-theory and G-theory of derived algebraic stacks
• A user's guide to co/cartesian fibrations
• Covariant Model Structures and Simplicial Localization
• Geometric higher groupoids and categories
• On some finiteness questions for algebraic stacks
• Stratified categories, geometric fixed points and a generalized Arone-Ching theorem
• Dg analogues of the Zuckerman functors and the dual Zuckerman functors I
• Local Theory for 2-Functors on Path 2-Groupoids
• Dendroidal Segal spaces and infinity-operads
• Parameters and duality for the metaplectic geometric Langlands theory
• Generators in formal deformations of categories
• A comparison of norm maps
• On the rational motivic homotopy category
• A homotopy coherent cellular nerve for bicategories
• p-adic J-homomorphisms and a product formula
• Rigidity in etale motivic stable homotopy theory
• Multiplicative structures on algebraic K-theory
• Loop Spaces and Langlands Parameters
• Equivariant Topology of Configuration Spaces
• A Quillen's Theorem A for strict $\infty$-categories I: the simplicial proof
• Homotopy L-infinity spaces
• A quantum Leray-Hirsch theorem for banded gerbes
• The weight complex functor is symmetric monoidal
• Enhanced adic formalism and perverse t-structures for higher Artin stacks
• Ribbon Graphs and Mirror Symmetry I
• A Cubical Language for Bishop Sets
• Eilenberg-MacLane spectra as equivariant Thom spectra
• Flat Base Change Formulas for $(\mathfrak{g},K)$-modules over Noetherian rings
• Dwyer-Kan homotopy theory of enriched categories
• Structured singular manifolds and factorization homology
• t-structures are normal torsion theories
• Higher-dimensional models of networks
• Relative Calabi-Yau completions
• Derived Algebraic Geometry
• The homotopy fixed points of the circle action on Hochschild homology
• Precobordism and cobordism
• Künneth formulas for motives and additivity of traces
• The accessibility rank of weak equivalences
• Tannaka duality and stable infinity-categories
• Yoneda lemma for enriched infinity categories
• Tensor triangular geometry of filtered objects and sheaves
• An Additivity theorem for cobordism categories
• Derived completion for comodules
• Regulators and cycle maps in higher-dimensional differential algebraic K-theory
• Beilinson-Bernstein localization over the Harish-Chandra center
• Homotopy coherent nerve in Deformation theory
• The homotopy theory of simplicial props
• Some recent advances in topological Hochschild homology
• Regular polygraphs and the Simpson conjecture
• Model Structures for Correspondences and Bifibrations
• Multiplicative parametrized homotopy theory via symmetric spectra in retractive spaces
• The topological chiral homology of the spherical category
• Derived Higher Hochschild Homology, Topological Chiral Homology and Factorization algebras
• Modules Over a Chiral Algebra
• Applications to A1-enumerative geometry of the A1-degree
• Derived categories of character sheaves
• The $\mathbb{R}$-Local Homotopy Theory of Smooth Spaces
• Dwyer-Kan localization revisited
• Categorical Milnor squares and K-theory of algebraic stacks
• Relative continuous K-theory and cyclic homology
• Regularity of structured ring spectra and localization in K-theory
• Model $\infty$-categories I: some pleasant properties of the $\infty$-category of simplicial spaces
• On the Sheafyness Property of Spectra of Banach Rings
• An infinite loop space machine for infinity-operads
• Counterexamples to Hochschild--Kostant--Rosenberg in characteristic $p$
• Periodizable motivic ring spectra
• Shifted symplectic reduction of derived critical loci
• A local-global principle for the telescope conjecture
• On a theorem of Braden
• Categorical Structures on Bundle Gerbes and Higher Geometric Prequantisation
• Equivariant motivic homotopy theory
• A Riemann--Hilbert correspondence for infinity local systems
• Simplicial spaces, lax algebras and the 2-Segal condition
• Hypersurface support and prime ideal spectra for stable categories
• Derived manifolds and Kuranishi models
• Homotopy theory of non-symmetric operads II: change of base category and left properness
• Bicategorical fibration structures and stacks
• Weight structures and the algebraic $K$-theory of stable $\infty$-categories
• Free algebras through Day convolution
• The special fiber of the motivic deformation of the stable homotopy category is algebraic
• Descent of Deligne-Getzler $\infty$-groupoids
• Dold-Kan correspondence for dendroidal abelian groups
• Microlocal sheaf categories and the $J$-homomorphism
• Algebraic Theories and (Infinity,1)-Categories
• Noncommutative calculus and operads
• Irreducible symplectic complex spaces
• Quasi-Categories vs. Segal Spaces: Cartesian Edition
• Topological equivariant coarse K-homology
• Univalence and completeness of Segal objects
• The homology of moduli stacks of complexes
• Generalised BGP reflection functors via the Grothendieck construction
• Motivic Tambara Functors
• Homotopy (Pre-)Derivators of Cofibration Categories and Quasi-Categories
• Moduli of $p$-adic representations of a profinite group
• Smith Ideals of Operadic Algebras in Monoidal Model Categories
• Universal factorization spaces and algebras
• Duality and small functors
• Tannaka duality over ring spectra
• Simplicial presheaves of coalgebras
• Introduction to Complete Segal Spaces
• Syntactic categories for dependent type theory: sketching and adequacy
• Algebraic models of homotopy types and the homotopy hypothesis
• Homotopy theory of monoids and derived localization
• Classifying theory for simplicial parametrized groups
• Segal Enriched Categories I
• Tate motives on Witt vector affine flag varieties
• Derived smooth stacks and prequantum categories
• Representations of finite groups on modules over K-theory (with an appendix by Akhil Mathew)
• A spectrum-level Hodge filtration on topological Hochschild homology
• Cohomology of the moduli stack of algebraic vector bundles
• The Beilinson regulator is a map of ring spectra
• Geometric constant term functor(s)
• Non-commutative Hilbert modular symbols
• Ginzburg algebras of triangulated surfaces and perverse schobers
• Derived Azumaya algebras and generators for twisted derived categories
• Super Lie n-algebra extensions, higher WZW models, and super p-branes with tensor multiplet fields
• Colocalizations of noncommutative spectra and bootstrap categories
• Enhanced twisted arrow categories
• Preorientations of the derived motivic multiplicative group
• A^1-homotopy invariance in spectral algebraic geometry
• The Local Joyal Model Structure
• The incidence comodule bialgebra of the Baez-Dolan construction
• Principal actions of stacky Lie groupoids
• Gluing pseudo functors via $n$-fold categories
• Slices of motivic Landweber spectra
• On categories of slices
• Algebraic Cobordism and Étale Cohomology
• A period map for global derived stacks
• Actions of Eilenberg-MacLane spaces on K-theory spectra and uniqueness of twisted K-theory
• Topological modular forms (aftern Hopkins, Miller, and Lurie)
• Towards a Thomason model structure on the category of strict n-categories
• Towards an extended/higher correspondence -- Generalised geometry, bundle gerbes and global Double Field Theory
• Stable moduli spaces of hermitian forms
• Fibred Fibration Categories
• On lifting univalence to the equivariant setting
• An Elementary Approach to Truncations
• Delta-discrete $G$-spectra and iterated homotopy fixed points
• Models for $(\infty ,n)$-categories and the cobordism hypothesis
• Notes on motivic infinite loop space theory
• The genuine operadic nerve
• Koszul duality for locally constant factorization algebras
• The tangent bundle of a model category
• Vanishing theorems for representation homology and the derived cotangent complex
• Multiplicative Structure in the Stable Splitting of $\Omega S{L}_n(\mathbb{C})$
• Equivariant localization and completion in cyclic homology and derived loop spaces
• Cubical models of $(\infty ,1)$-categories
• Marked colimits and higher cofinality
• K-theory of endomorphisms via noncommutative motives
• The universal property of derived geometry
• A short note on infinity-groupoids and the period map for projective manifolds
• Additive C*-categories and K-theory
• Some Higher Coalgebra
• Kleisli Database Instances
• The A_infty de Rham theorem and integration of representations up to homotopy
• The Cobordism Hypothesis in Dimension 1
• Descent properties of the topological chiral homology
• Deligne groupoid revisited
• Some remarks on topological $K$-theory of dg categories
• The stable hull of an exact $\infty$-category
• Spherical adjunctions of stable $\infty$-categories and the relative S-construction
• On the uniqueness of infinity-categorical enhancements of triangulated categories
• Homotopy theory in a quasi-abelian category
• Morita homotopy theory for $(\infty ,1)$-categories and $\infty$-operads
• On the automorphic sheaves for GSp_4
• The homotopy limit problem and the cellular Picard group of Hermitian $K$-theory
• Localization for coarse homology theories
• Proper Orbifold Cohomology
• Higher semiadditive Grothendieck-Witt theory and the $K(1)$-local sphere
• Semi-infinite cohomology and Kazhdan-Lusztig equivalence at positive level
• Galois Descent for Real Spectra
• Dg analogues of the Zuckerman functors and the dual Zuckerman functors II
• Small object arguments, plus-construction, and left-exact localizations
• Equivariant dendroidal sets and simplicial operads
• The semi-infinite intersection cohomology sheaf
• Deformation theory of perfect complexes and traces
• Model $\infty$-categories II: Quillen adjunctions
• Concrete Categories in Homotopy Type Theory
• Recent progress in geometric Langlands theory
• Uniformization of semistable bundles on elliptic curves
• The global derived period map
• Perverse schobers and the Algebra of the Infrared
• Spherical monadic adjunctions of stable infinity categories
• The Atiyah-Bott formula and connectivity in chiral Koszul duality
• $(\infty ,1)$-Categorical Comprehension Schemes
• Exponentiable Higher Toposes
• Local Complete Segal Spaces
• Quasicategories of Frames of Cofibration Categories
• Derived Hall algebras for stable homotopy theories
• A model structure on the category of small categories for coverings
• Algebraic Definition of weak ($\infty$; n)-Categories
• Unwinding the relative Tate diagonal
• Homotopy coherent theorems of Dold-Kan type
• The Devinatz-Hopkins Theorem via Algebraic Geometry
• Derived gluing construction of chiral algebras
• Geometric Satake, Springer correspondence, and small representations II
• Twisted differential KO-theory
• Nilpotence in normed MGL-modules
• Complex K-theory of mirror pairs
• The Duskin nerve of 2-categories in Joyal's cell category Theta_2
• Descent Theory and Mapping Spaces
• The Operadic Nerve, Relative Nerve, and the Grothendieck Construction
• Classifying spaces of infinity-sheaves
• Filter Quotients and Non-Presentable $(\infty ,1)$-Toposes
• Derived ${\mathcal{O}}_k$-adic geometry and derived Raynaud localization theorem
• Higher colimits, derived functors and homology
• The zeroth P^1-stable homotopy sheaf of a motivic space
• Differential characters as stacks and prequantization
• Quillen cohomology of enriched operads
• Motivic and Étale Spanier-Whitehead duality and the Becker-Gottlieb transfer
• The affine Hecke category is a monoidal colimit
• Synthetic fibered $(\infty ,1)$-category theory
• Model $\infty$-categories III: the fundamental theorem
• Weak cartesian properties of simplicial sets
• Moduli stack of oriented formal groups and periodic complex bordism
• The two out of three property in ind-categories and a convenient model category of spaces
• A Torus Theorem for homotopy nilpotent groups
• Singular chains on topological stacks
• Hearts and towers in stable infinity-categories
• $C^{\ast }$-algebraic drawings of dendroidal sets
• Completeness for monads and theories
• Categorical Donaldson-Thomas theory for local surfaces: $\mathbb{Z}/2$-periodic version
• Koszul duality between $E_n$-algebras and coalgebras in a filtered category
• Simplicial localization of homotopy algebras over a prop
• Mixed motives and quotient stacks: Abelian varieties
• Tame twistings and $\Theta$-data
• The May filtration on THH and faithfully flat descent
• Enriched infinity categories I: enriched presheaves
• Moduli of framed formal curves
• Adjoining roots in homotopy theory
• Goerss--Hopkins obstruction theory for $\infty$-categories
• Nerves of 2-categories and 2-categorification of $(\infty ,2)$-categories
• Parametrized geometric cobordism and smooth Thom stacks
• The universal Hall bialgebra of a double 2-Segal space
• Localizing infinity-categories with hypercovers
• Type-amalgamation properties and polygroupoids in stable theories
• From Operads to Dendroidal Sets
• Inner horns for 2-quasi-categories
• Parallel Transport on Higher Loop Spaces
• Monoidal Infinity Category of Complexes from Tannakian Viewpoint
• Combinatorial model categories are equivalent to presentable quasicategories
• Bousfield-Segal spaces
• An Extension of the Kazhdan-Lusztig Equivalence
• Moduli stack of oriented formal groups and the chromatic filtration
• Cubical n-Categories and Finite Limits Theories
• Graded algebras, projective spectra and blow-ups in derived algebraic geometry
• Topological Hochschild homology and Zeta-values
• Frobenius and the derived centers of algebraic theories
• The Euler characteristic of a bicategory and the product formula for fibered bicategories
• Derived deformation theory of algebraic structures
• Derived deformation rings allowing congruences]{Derived deformation rings allowing congruences
• Topoi of parametrized objects
• Presentable $(\infty ,n)$-categories
• Higher sheaf theory I: Correspondences
• Perverse sheaves on Riemann surfaces as Milnor sheaves
• Period Rings with Big Coefficients and Application II
• On 2-final 2-functors
• Homotopy fixed points for profinite groups emulate homotopy fixed points for discrete groups
• Small presentations of model categories and Vopěnka's principle
• Perfectoid Diamonds and n-Awareness. A Meta-Model of Subjective Experience
• Homotopical presentations of braid groups via reduced lifts
• A colimit presentation of $\mathcal{D}(G(K))$ via the Bott-Samelson hypercover
• On a notion of ring groupoid
• Rigidification and the Coherent Nerve for Enriched Quasicategories
• Notes on the Joyal model structure
• Higher dimensional algebras via colored PROPs
• Deligne--Lusztig duality on the moduli stack of bundles
• On lax limits in infinity categories
• Nearby cycles on Drinfeld-Gaitsgory-Vinberg Interpolation Grassmannian and long intertwining functor
• Diagrams, Fibrations, and the Decomposition of Colimits
• Some characterizations of acyclic maps
• Differential calculus of Hochschild pairs for infinity-categories
• Accessible categories, set theory, and model theory: an invitation
• Dependent products and 1-inaccessible universes
• A Fubini rule for $\infty$-coends
• $L^{\prime }$-localization in an $\infty$-topos
• Etale homotopy theory of non-archimedean analytic spaces
• So, what is a derived functor?
• Topological rigidification of schemes
• Weakly globular Tamsamani N-categories and their rigidification
• 2-fold complete Segal operads
• K-theory of non-archimedean rings I
• Cocycles in Local Higher Category Theory
• Ample line bundles, global generation and $K_0$ on quasi-projective derived schemes
• Equivalence of models for equivariant $(\infty ,1)$-categories
• An integral model structure and truncation theory for coherent group actions
• A note on commutative algebras and their modules in quasicategories
• 2-Modules and the Representation of 2-Rings
• Categorical Moy-Prasad theory
• Solving Homotopy Domain Equations
• Operads and Maurer-Cartan spaces
• Automorphic gluing functor in Betti Geometric Langlands
• On the Dundas-Goodwillie-McCarthy theorem
• Traces for factorization homology in dimension 1
• Gerbes in Geometry, Field Theory, and Quantisation
• A stable $\infty$-category for equivariant $KK$-theory
• Joyal's cylinder conjecture
• Filtered formal groups, Cartier duality, and derived algebraic geometry
• K-theoretic invariants of Hamiltonian fibrations
• On extension of the motivic cohomology beyond smooth schemes
• Spectral Sequences in $(\infty ,1)$-Categories
• Localization and flexibilization in symplectic geometry
• Abelian Groups in omega-categories
• Euler characteristic and homotopy cardinality
• On window theorem for categorical Donaldson-Thomas theories on local surfaces and its applications
• Morse theory with homotopy coherent diagrams
• Workshop on the homotopy theory of homotopy theories
• Geometric derived Hall algebra
• The $A_{\infty }$-structure of the index map
• Duality for Topological Modular Forms
• Abstract homotopical methods for theoretical computer science
• Cubical model categories and quasi-categories
• From Ohkawa to strong generation via approximable triangulated categories -- a variation on the theme of Amnon Neeman's Nagoya lecture series
• Higher Lawvere theories
• Enriched Sets and Higher Categories
• A variant of algebraic K-theory
• Discrete G-Spectra and embeddings of module spectra
• On duoidal $\infty$-categories
• Segal-type models of higher categories
• Versal dg deformation of Calabi--Yau manifolds
• On the Farrell-Jones conjecture for localising invariants
• Categories of modules and their deformations
• Higher stacks as diagrams
• On the construction of limits and colimits in $\infty$-categories
• Integration of Voevodsky motives
• Sylow theorems for $\infty$-groups
• Higher Theory and the Three Problems of Physics
• Tannakization of quasi-categories and monadic descent
• A Geometric Proof of the Feigin-Frenkel Theorem
• Noncommutative derived Poisson reduction
• Factorization systems in $\infty$-categories
• A higher Grothendieck construction
• On the structure of simplicial categories associated to quasi-categories
• Zariski-local framed ${\mathbb{A}}^1$-homotopy theory
• Modulus sheaves with transfers
• A sketch for derivators
• Extended Field Theories as higher Kaluza-Klein theories
• A Quillen model category structure on some categories of comonoids
• Goodwillie's cosimplicial model for the space of long knots and its applications
• Prestacks of Tate type
• Cellular objects and Shelah's singular compactness theorem
• Coherent cochain complexes and Beilinson t-structures, with an appendix by Achim Krause
• From Six Functors Formalisms to Derived Motivic Measures
• Crossed extensions and equivalences of topological 2-groupoids
• Derived bi-duality via homotopy limit
• From weak cofibration categories to model categories
• $p$-torsion étale sheaves on the Jacobian of a curve
• Algebraic $K$-theory of $\text{THH}({\mathbb{F}}_p)$
• Comparison Between Different Topological Models of Concurrency
• Basic Set Theory and Algebra: Hints on Representation, Topology, Geometry, Analysis
• Modules over the de Rham cohomology spectrum
• The Fundamental Infinity-Groupoid of a Parametrized Family
• The category of $\pi$-finite spaces
• A proof of the Dold$-$Thom theorem via factorization homology
• Categories of orbit types for proper Lie groupoids
• Stabilization and costabilization with respect to an action of a monoidal category
• Quillen cohomology of $(\infty ,2)$-categories
• Spectral Networks and Non-abelianization
• Colimits of accessible categories
• Sheaves of Higher Categories on Generalised Spaces
• Formality of little disks and algebraic geometry
• Witt differentials in the h-topology
• Dualizable objects in stratified categories and the 1-dimensional bordism hypothesis for recollements
• Internal $\infty$-Categorical Models of Dependent Type Theory: Towards 2LTT Eating HoTT
• On D-modules of categories I
• $\infty$-cosheafification
• Some refinements of the Deligne-Illusie theorem
• Segal Topoi and Natural Phenomena: Universality of Physical Laws
• On a fat small object argument
• Integral representation theorems for DQ-modules
• Enhanced bivariant homology theory attached to six functor formalism
• Pontryagin duality for varieties over $p$-adic fields
• Higher Dimensional Homology Algebra III:Projective Resolutions and Derived 2-Functors in (2-SGp)
• t-structures on stable infinity-categories
• Comonadic Coalgebras and Bousfield Localization
• Introduction to Abstract Homotopy Theory
• A survey of models for $(\infty ,n)$-categories
• Homology of categories via polygraphic resolutions