9 citations · 25 across the 7 of their papers we have counts for
7 papers
Quillen Theorems Bn for homotopy pullbacks of (infinity, k)-categories
C. Barwick, D. M. Kan
We extend the Quillen Theorem Bn for homotopy fibers of Dwyer, et al. to similar results for homotopy pullbacks and note that these results imply similar results for zigzags in the…
Partial model categories and their simplicial nerves
C. Barwick, D. M. Kan
In this note we consider partial model categories, by which we mean relative categories that satisfy a weakened version of the model category axioms involving only the weak equival…
n-Relative Categories
C. Barwick, D. M. Kan
We introduce, for every positive integer n, the notion of an n-relative category and show that the category of the small n-relative categories is a model for the homotopy theory of…
A Quillen theorem Bn for homotopy pullbacks
C. Barwick, D. M. Kan
We prove an extension of the Quillen Theorem Bn for homotopy fibres to a similar result for homotopy pullbacks and use this to obtain sufficient conditions on a pullback diagram of…
A Thomason-like Quillen equivalence between quasi-categories and relative categories
C. Barwick, D. M. Kan
We describe a Quillen equivalence between quasi-categories and relative categories which is surprisingly similar to Thomason's Quillen equivalences between simplicial sets and cate…
In the category of relative categories the Rezk equivalences are exactly the DK-equivalences
C. Barwick, D. M. Kan
In a previous paper we lifted Charles Rezk's complete Segal model structure on the category of simplicial spaces to a Quillen equivalent one on the category of "relative categories…