The (2,1)-category of small coherent categories

Abstract

There is a well-known correspondence between coherent theories (and their interpretations) and coherent categories (resp. functors), hence the (2,1)-category $\mathbf{Co}{\mathbf{h}}_{\sim }$ (of small coherent categories, coherent functors and all natural isomorphisms) is of logical interest. We prove that this category admits all small 2-limits and 2-colimits (in the ($\infty$,1)-categorical sense), and prove a 2-categorical small object argument to provide weak factorisation systems for coherent functors.

References in corpus (1)

• Interchange of filtered 2-colimits and finite 2-limits