69 citations · 225 across the 25 of their papers we have counts for
26 papers · 1 filter
A constructive approach to the double-categorical small object argument
Benno van den Berg, John Bourke, Paul Seip
Bourke and Garner described how to cofibrantly generate algebraic weak factorisation systems by a small double category of morphisms. However they did not give an explicit construc…
A recognition criterion for lax-idempotent pseudomonads
John Bourke
We describe a simple criterion which makes it easy to recognise when a pseudomonad is lax-idempotent. The criterion concerns the behaviour of colax bilimits of arrows - certain com…
Enhanced 2-categorical structures, two-dimensional limit sketches and the symmetry of internalisation
Nathanael Arkor, John Bourke, Joanna Ko
Many structures of interest in two-dimensional category theory have aspects that are inherently strict. This strictness is not a limitation, but rather plays a fundamental role in…
On -categorical -cosmoi
John Bourke, Stephen Lack
Recently Riehl and Verity have introduced -cosmoi, which are certain simplicially enriched categories with additional structure. In this paper we investigate those …
A skew approach to enrichment for Gray-categories
John Bourke, Gabriele Lobbia
It is well known that the category of Gray-categories does not admit a monoidal biclosed structure that models weak higher-dimensional transformations. In this paper, the first of…
An orthogonal approach to algebraic weak factorisation systems
John Bourke
We describe an equivalent formulation of algebraic weak factorisation systems, not involving monads and comonads, but involving double categories of morphisms equipped with a lifti…