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arXiv · 2003.06375

Accessible aspects of 2-category theory

John Bourke
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Abstract

Categorical structures and their pseudomaps rarely form locally presentable 2-categories in the sense of Cat-enriched category theory. However, we show that if the categorical structure in question is sufficiently weak (such as the structure of monoidal, but not strict monoidal, categories) then the 2-category in question is accessible. Furthermore, we explore the flexible limits that such 2-categories possess and their interaction with filtered colimits.

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John Bourke. 2020-03-13. Accessible aspects of 2-category theory. https://doi.org/10.1016/j.jpaa.2020.106519

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