37 citations · 56 across the 9 of their papers we have counts for
9 papers
A convenient model category for bicategories
Alexander Campbell
We introduce and study the model category of flexible -categories, which is Quillen equivalent to Lack's model category of -categories, but enjoys several excellent propertie…
Parity complexes redux
Alexander Campbell
We fix the notion of parity complex by a judicious selection from among the axioms originally considered by Street. We show that parity complexes so defined, together with the morp…
Equivalence via surjections
Tom Leinster
Many types of categorical structure obey the following principle: the natural notion of equivalence is generated, as an equivalence relation, by identifying with when there…
Joyal's cylinder conjecture
Alexander Campbell
For each pair of simplicial sets and , the category of cylinders (also called correspondences) from to admits a model structure induced from Joya…
A homotopy coherent cellular nerve for bicategories
Alexander Campbell
The subject of this paper is a nerve construction for bicategories introduced by Leinster, which defines a fully faithful functor from the category of bicategories and normal pseud…
A counterexample in quasi-category theory
Alexander Campbell
We give an example of a morphism of simplicial sets which is a monomorphism, bijective on 0-simplices, and a weak categorical equivalence, but which is not inner anodyne. This answ…
On truncated quasi-categories
Alexander Campbell, Edoardo Lanari
For each , a quasi-category is said to be -truncated if its hom-spaces are -types. In this paper we study the model structure for -truncated quasi-categorie…
How strict is strictification?
Alexander Campbell
The subject of this paper is the higher structure of the strictification adjunction, which relates the two fundamental bases of three-dimensional category theory: the $\mathbf{Gray…
Skew-enriched categories
Alexander Campbell
This paper introduces a skew variant of the notion of enriched category, suitable for enrichment over a skew-monoidal category, the main novelty of which is that the elements of th…