Related papers: Gray-categories model algebraic tricategories
We put a model structure on the category of categories internal to simplicial sets whose weak equivalences are reflected by the nerve functor to bisimplicial sets with Rezk's model structure. This model structure is shown to be Quillen…
Homotopy 3-types can be modelled algebraically by Tamsamani's weak 3-groupoids as well as, in the path-connected case, by cat^2-groups. This paper gives a comparison between the two models in the path-connected case. This leads to two…
For each $n \in \mathbb{N} \cup \{\infty\}$, diagrammatic sets admit a model structure whose fibrant objects are the diagrammatic $(\infty, n)$- categories. They also support a notion of Gray product given by the Day convolution of a…
Weakly globular double categories are a model of weak $2$-categories based on the notion of weak globularity, and they are known to be suitably equivalent to Tamsamani $2$-categories. Fair $2$-categories, introduced by J. Kock, model weak…
We construct on the category of diffeological spaces a Quillen model structure having smooth weak homotopy equivalences as the class of weak equivalences.
We study a new type of higher categorical structure, called weakly globular n-fold category, previously introduced by the author. We show that this structure is a model of weak n-categories by proving that it is suitably equivalent to the…
We study locally presentable categories equipped with a cofibrantly generated weak factorization system. Our main result is that these categories are closed under 2-limits, in particular under pseudopullbacks. We give applications to…
We study the simplicial coalgebra of chains on a simplicial set with respect to three notions of weak equivalence. To this end, we construct three model structures on the category of reduced simplicial sets for any commutative ring R. The…
This text develops a homotopy theory of 2-categories analogous to Grothendieck's homotopy theory of categories developed in "Pursuing Stacks". We define the notion of "basic localizer of 2-Cat", 2-categorical generalization of…
We investigate fibrancy conditions in the Thomason model structure on the category of small categories. In particular, we show that the category of weak equivalences of a partial model category is fibrant. Furthermore, we describe…
In this paper we obtain several model structures on {\bf DblCat}, the category of small double categories. Our model structures have three sources. We first transfer across a categorification-nerve adjunction. Secondly, we view double…
In this paper we present cartesian structure for symmetric Gray-monoidal double categories. To do this we first introduce locally cubical Gray categories, which are three-dimensional categorical structures analogous to classical, locally…
To a bicomplex one can associate two natural filtrations, the column and row filtrations, and then two associated spectral sequences. This can be generalized to $N$-multicomplexes. We present a family of model category structures on the…
Over the recent years, the theory of rewriting has been used and extended in order to provide systematic techniques to show coherence results for strict higher categories. Here, we investigate a further generalization to Gray categories,…
We construct a Quillen model structure on the category of spectral categories, where the weak equivalences are the symmetric spectra analogue of the notion of equivalence of categories.
We construct a model structure on the category of cubical sets with connections whose cofibrations are the monomorphisms and whose fibrant objects are defined by the right lifting property with respect to inner open boxes, the cubical…
We introduce a notion of quasi-weak equivalences associated with weak-equivalences in an exact category. It gives us a delooping for (idempotent complete) exact categories and a condition that the negative $K$-group of an exact category…
In this note, we study the connection between Gray tensor product and suspension. We derive a characterization of weak equivalences as fully faithful and essentially surjective functors. We construct the $co$ duality, a weak involution that…
We show that weak monoidal Quillen equivalences induce equivalences of symmetric monoidal $\infty$-categories with respect to the Dwyer-Kan localization of the symmetric monoidal model categories. The result will induce a Dold-Kan…
We present an efficient and user-friendly method for constructing any cofibrantly generated model structure on the category of double categories whose trivial fibrations are the "canonical" ones: the double functors which are surjective on…