Accessible aspects of 2-category theory
arXiv:2003.06375 · doi:10.1016/j.jpaa.2020.106519
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.
References in corpus (10)
- Sheafifiable homotopy model categories
- Understanding the small object argument
- A Quillen model structure for Gray-categories
- Icons
- Two-dimensional models of type theory
- Homotopy-theoretic aspects of 2-monads
- Enhanced 2-categories and limits for lax morphisms
- Categorical notions of fibration
- Enriched weakness
- Adjoint functor theorems for homotopically enriched categories