nLab
locally full sub-2-category
Contents
Context
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

Notions of subcategory
Contents
Definition
A locally full sub 2-category is one whose embedding 2-functor $C\to D$ is locally fully faithful . This means that each $C(c_1,c_2)$ is a full subcategory of $D(c_1, c_2)$ .

Examples
The sub-2-category of $Prof_{rep} \hookrightarrow$ Prof on all representable profunctor s is locally full.

The sub-2-category of the 2-category $T Alg_l$ of algebras for a 2-monad and lax morphisms between them contains, as a locally full sub-2-category, the 2-category $T Alg_p$ of algebras and pseudo morphisms (or of strict morphisms, if $T$ is strict).

Both of these examples are also wide subcategories . A wide and locally full sub-2-category is equivalent to an F-category . See also 2-category equipped with proarrows .

Last revised on November 18, 2011 at 10:56:24.
See the history of this page for a list of all contributions to it.