Definitions
Transfors between 2-categories
Morphisms in 2-categories
Structures in 2-categories
Limits in 2-categories
Structures on 2-categories
A semiflexible limit is a strict 2-limit whose weight is semiflexible (defined below). The semiflexible weights are precisely those weights whose limits are bilimits.
All flexible limits, hence also PIE-limits and strict pseudo-limits, are semiflexible.
The class of semiflexible weights is a saturated class of limits.
Let be a small strict 2-category. Write for the strict 2-category of strict 2-functors, strict 2-natural transformations, and modifications, and for the strict 2-category of strict 2-functors, pseudonatural transformations, and modifications. The inclusion
(as a wide subcategory) has a strict left adjoint , which is the pseudo morphism classifier for an appropriate strict 2-monad. Therefore, for any functor , we have such that pseudonatural transformations are in natural bijection with strict 2-natural transformations .
The counit of this adjunction is a canonical strict 2-natural transformation . We say that is semiflexible if this transformation admits a pseudo-section? (equivalent is an equivalence) in .
Greg J. Bird, Max Kelly, John Power, Ross Street, Flexible limits for 2-categories, Journal of Pure and Applied Algebra 61 1 (1989) 1-27 [doi:10.1016/0022-4049(89)90065-0]
John Bourke and Richard Garner, On semiflexible, flexible and pie algebras, Journal of Pure and Applied Algebra 217.2 (2013): 293-321.
Created on June 12, 2024 at 09:35:02. See the history of this page for a list of all contributions to it.