nLab
locally full sub-2-category

Contents

Definition

A locally full sub 2-category is one whose embedding 2-functor CDC\to D is locally fully faithful. This means that each C(c 1,c 2)C(c_1,c_2) is a full subcategory of D(c 1,c 2)D(c_1, c_2).

Examples

  • The sub-2-category of Prof repProf_{rep} \hookrightarrow Prof on all representable profunctors is locally full.

  • The sub-2-category of the 2-category TAlg lT Alg_l of algebras for a 2-monad and lax morphisms between them contains, as a locally full sub-2-category, the 2-category TAlg pT Alg_p of algebras and pseudo morphisms (or of strict morphisms, if TT 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.

Revised on November 18, 2011 10:56:24 by Urs Schreiber (217.232.18.193)