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arXiv · 2104.13239

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

Kristóf Kanalas
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Abstract

There is a well-known correspondence between coherent theories (and their interpretations) and coherent categories (resp. functors), hence the (2,1)-category $\mathbf{Coh_{\sim}}$ (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.

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Kristóf Kanalas. 2021-04-27. The (2,1)-category of small coherent categories. https://arxiv.org/abs/2104.13239

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