164 citations · 1.4k across the 51 of their papers we have counts for
5 papers · 1 filter
Lex colimits
Richard Garner, Stephen Lack
Many kinds of categorical structure require the existence of finite limits, of colimits of some specified type, and of "exactness" conditions between the finite limits and the spec…
Grothendieck quasitoposes
Richard Garner, Stephen Lack
A full reflective subcategory E of a presheaf category [C*,Set] is the category of sheaves for a topology j on C if and only if the reflection preserves finite limits. Such an E is…
Enhanced 2-categories and limits for lax morphisms
Stephen Lack, Michael Shulman
We study limits in 2-categories whose objects are categories with extra structure and whose morphisms are functors preserving the structure only up to a coherent comparison map, wh…
An embedding theorem for adhesive categories
Stephen Lack
Adhesive categories are categories which have pushouts with one leg a monomorphism, all pullbacks, and certain exactness conditions relating these pushouts and pullbacks. We give a…
Idempotent splittings, colimit completion, and weak aspects of the theory of monads
Gabriella Böhm, Stephen Lack, Ross Street
We show that some recent constructions in the literature, named `weak' generalizations, can be systematically treated by passing from 2-categories to categories enriched in the Car…