13 citations · 50 across the 27 of their papers we have counts for
30 papers
Fractured Structures in Condensed Mathematics
Nima Rasekh, Qi Zhu
We construct a fractured structure, in the sense of Lurie, on the -topos of condensed anima. This fractured structure allows us to better comprehend various properties of c…
Simplicial Homotopy Type Theory is not just Simplicial: What are -Categories?
Nima Rasekh
-category theory was originally developed in the context of classical homotopy theory using standard set theoretical assumptions, but has since been extended to a variety o…
Non-Standard Models of Homotopy Type Theory
Nima Rasekh
Homotopy type theory is a modern foundation for mathematics that introduces the univalence axiom and is particularly suitable for the study of homotopical mathematics and its forma…
Filter Quotient Model Structures
Nima Rasekh
The filter quotient construction is a particular instance of a filtered colimit of categories. It has primarily been considered in the context of categorical logic, where it has be…
Cosmological Unstraightening
Nima Rasekh
The unstraightening construction due to Lurie establishes an equivalence between presheaves and fibrations, using one prominent model of -categories, namely quasi-categ…
-Limits II: Comparison across models
Lyne Moser, Martina Rovelli, Nima Rasekh
We show that the notion of -limit defined using the enriched approach and the one defined using the internal approach coincide. We also give explicit constructions of v…
Insights From Univalent Foundations: A Case Study Using Double Categories
Nima Rasekh, Niels van der Weide, Benedikt Ahrens +1
Category theory unifies mathematical concepts, aiding comparisons across structures by incorporating objects and morphisms, which capture their interactions. It has influenced area…
-Limits I: Definition and first consistency results
Lyne Moser, Nima Rasekh, Martina Rovelli
We give a model-independent definition of limits for diagrams valued in an -category. We show that this definition is compatible with the existing notion of homotopy 2-…
Univalent Double Categories
Niels van der Weide, Nima Rasekh, Benedikt Ahrens +1
Category theory is a branch of mathematics that provides a formal framework for understanding the relationship between mathematical structures. To this end, a category not only inc…
An -categorical straightening-unstraightening construction
Lyne Moser, Nima Rasekh, Martina Rovelli
We provide an -categorical version of the straightening-unstraightening construction, asserting an equivalence between the -category of double $(\infty,n-1)…
A homotopy coherent nerve for -categories
Lyne Moser, Nima Rasekh, Martina Rovelli
In the case of -categories, the homotopy coherent nerve gives a right Quillen equivalence between the models of simplicially enriched categories and of quasi-categories…
Shadows are Bicategorical Traces
Kathryn Hess, Nima Rasekh
Hochschild homology has proved to be an important invariant in algebra and homotopy theory, in particular due to its relevance in algebraic -theory and fixed point theory, leadi…
Yoneda Lemma for -Simplicial Spaces
Nima Rasekh
For a small category we define fibrations of simplicial presheaves on the category , which we call localized -left fibration. We show…
Constructing Coproducts in locally Cartesian closed -Categories
Jonas Frey, Nima Rasekh
We prove that every locally Cartesian closed -category with subobject classifier has a strict initial object and disjoint and universal binary coproducts.
Univalence in Higher Category Theory
Nima Rasekh
Univalence was first defined in the setting of homotopy type theory by Voevodsky, who also (along with Kapulkin and Lumsdaine) adapted it to a model categorical setting, which was…
Cartesian Fibrations of Complete Segal Spaces
Nima Rasekh
Cartesian fibrations were originally defined by Lurie in the context of quasi-categories and are commonly used in -category theory to study presheaves valued in $(\inft…
Quasi-Categories vs. Segal Spaces: Cartesian Edition
Nima Rasekh
We prove that four different ways of defining Cartesian fibrations and the Cartesian model structure are all Quillen equivalent: On marked simplicial sets, on bisimplicial spaces,…
The cotangent complex and Thom spectra
Nima Rasekh, Bruno Stonek
The cotangent complex of a map of commutative rings is a central object in deformation theory. Since the 1990s, it has been generalized to the homotopical setting of -rin…
Filter Quotients and Non-Presentable -Toposes
Nima Rasekh
We define filter quotients of -categories and prove that filter quotients preserve the structure of an elementary -topos and in particular lift the filter q…
Thom spectra, higher and tensors in -categories
Nima Rasekh, Bruno Stonek, Gabriel Valenzuela
Let be a map of -groups, where denotes the Picard space of an -ring spectrum . We determine the tensor $X\otimes_R…
An Elementary Approach to Truncations
Nima Rasekh
We study truncated objects using elementary methods. Concretely, we use universes and the resulting natural number object to define internal truncation levels and prove they behave…
Yoneda Lemma for Elementary Higher Toposes
Nima Rasekh
We prove the Yoneda lemma inside an elementary higher topos, generalizing the Yonda lemma for spaces.
Every Elementary Higher Topos has a Natural Number Object
Nima Rasekh
We prove that every elementary -topos has a natural number object. We achieve this by defining the loop space of the circle and showing that we can construct a natural…
Complete Segal Objects
Nima Rasekh
We define complete Segal objects, which play the role of internal higher category objects. Then we study them using representable Cartesian fibrations, in particular defining adjun…