7 citations · 13 across the 5 of their papers we have counts for
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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…
A characterization of simplicial localization functors
C. Barwick, D. M. Kan
We characterize simplicial localization functors among relative functors from relative categories to simplicial categories as any choice of homotopy inverse to the delocalization f…