15 citations · 73 across the 25 of their papers we have counts for
26 papers · 1 filter
Rewriting and presentations of quasicategories
Simon Henry
We show that the methods of rewriting theory to establish coherence theorems can applied at the level of quasicategories. More precisely, for any category C which admits a presenta…
Homotopy Languages
César Bardomiano Martínez, Simon Henry
We attach to each weak model category a class of first order formulas about the fibrant objects of whose validity is invariant under homotopies and weak…
A Classifying groupoid for compact Hausdorff locales
Simon Henry, Christopher Townsend
We construct a localic groupoid such that for any locale the category of compact Hausdorff locales in the topos of sheaves over is equivalent to a categor…
Compact Hausdorff Locales in presheaf toposes
Simon Henry, Christopher Townsend
We prove that for any small category , the category of compact Hausdorff locales in the presheaf topos , is…
Higher Theories and Monads
Simon Henry, Nicholas J. Meadows
We extend Bourke and Garner's idempotent adjunction between monads and pretheories to the framework of -categories and we use this to prove many classical results about mon…
The effective model structure and -groupoid objects
Nicola Gambino, Simon Henry, Christian Sattler +1
For a category with finite limits and well-behaved countable coproducts, we construct a model structure, called the effective model structure, on the category of simpl…
Minimal model structures
Simon Henry
We prove, without set theoretic assumptions, that every locally presentable category C endowed with a tractable cofibrantly generated class of cofibrations has a unique minimal (or…
Combinatorial and accessible weak model categories
Simon Henry
In a previous work, we have introduced a weakening of Quillen model categories called weak model categories. They still allow all the usual constructions of model category theory,…
A constructive account of the Kan-Quillen model structure and of Kan's Ex functor
Simon Henry
We give a fully constructive proof that there is a proper cartesian -combinatorial model structure on the category of simplicial sets, whose generating cofibrations and trivial…
On the homotopy hypothesis in dimension 3
Simon Henry, Edoardo Lanari
We show that if the canonical left semi-model structure on the category of Grothendieck -groupoids exists, then it satisfies the homotopy hypothesis, i.e. the associated $(\inft…
Towards a constructive simplicial model of Univalent Foundations
Nicola Gambino, Simon Henry
We provide a partial solution to the problem of defining a constructive version of Voevodsky's simplicial model of univalent foundations. For this, we prove constructive counterpar…
An abstract elementary class non-axiomatizable in
Simon Henry
We show that for any uncountable cardinal , the category of sets of cardinality at least and monomorphisms between them cannot appear as the category of point of a topos, in…
Regular polygraphs and the Simpson conjecture
Simon Henry
We prove Carlos Simpson's "semi-strictification" (or "weak unit") conjecture in the case of infinity-groupoids. More precisely, we introduce two precise versions of the conjecture,…
Weak model categories in classical and constructive mathematics
Simon Henry
We introduce a notion of "weak model category" which is a weakening of the notion of Quillen model category, still sufficient to define a homotopy category, Quillen adjunctions, Qu…
Non-unital polygraphs form a presheaf category
Simon Henry
We prove, as claimed by A.Carboni and P.T.Johnstone, that the category of non-unital polygraphs, i.e. polygraphs where the source and target of each generator are not identity arro…
The localic Istropy group of a topos
Simon Henry
It has been shown by J.Funk, P.Hofstra and B.Steinberg that any Grothendieck topos T is endowed with a canonical group object, called its isotropy group, which acts functorially on…
The convolution algebra of an absolutely locally compact topos
Simon Henry
We introduce a class of toposes called "absolutely locally compact" toposes and of "admissible" sheaf of rings over such toposes. To any such ringed topos we atta…
Algebraic models of homotopy types and the homotopy hypothesis
Simon Henry
We introduce and study a notion of cylinder coherator similar to the notion of Grothendieck coherator which define more flexible notion of weak infinity groupoids. We show that eac…
Complete C*-categories and a topos theoretic Green-Julg theorem
Simon Henry
We investigate what would be a correct definition of categorical completeness for C*-categories and propose several variants of such a definition that make the category of Hilbert…
On toposes generated by cardinal finite objects
Simon Henry
We give a characterizations of toposes which admit a generating family of objects which are internally cardinal finite (i.e. Kuratowski finite and decidable) in terms of "topologic…
A Geometric Bohr topos
Simon Henry
In this short note, we construct a variant of the Bohr topos of a C*-algebra which takes into account the topology of the algebra in a finer way and such that this construction is…
Toward a non-commutative Gelfand duality: Boolean locally separated toposes and Monoidal monotone complete -categories
Simon Henry
** Draft Version ** To any boolean topos one can associate its category of internal Hilbert spaces, and if the topos is locally separated one can consider a full subcategory of squ…
Constructive Gelfand duality for non-unital commutative C*-algebras
Simon Henry
We prove constructive versions of various usual results related to the Gelfand duality. Namely, that the constructive Gelfand duality extend to a duality between commutative nonuni…
Measure theory over boolean toposes
Simon Henry
In this paper we develop a notion of measure theory over boolean toposes which is analogous to noncommutative measure theory, i.e. to the theory of von Neumann algebras. This is pa…