3 papers
math.CT2026
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…
math.CT2025
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…
math.CT2024
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…