nLab
isocofibration
Contents
Context
Category theory
2-category theory
2-category theory

Definitions

Transfors between 2-categories

Morphisms in 2-categories

Structures in 2-categories

Limits in 2-categories

Structures on 2-categories

Contents
Idea
A morphism $f:A\to B$ in a strict 2-category $K$ is an isocofibration if the corresponding morphism $B\to A$ in $K^{op}$ is an isofibration .

Examples
In Cat (and Grpd ), the isocofibrations are the functors which are injective on objects . There they are the cofibrations in the canonical model structure on Cat (on Grpd ).

However, a general 2-category has two candidates for a canonical model structure, one involving the isofibrations and one the isocofibrations, and in general the two may not be the same.

Last revised on November 1, 2023 at 06:46:49.
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