locally full sub-2-category
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
locally full sub 2-category is one whose embedding 2-functor is C → D locally fully faithful. This means that each is a C ( c 1 , c 2 ) full subcategory of . D ( c 1 , c 2 ) Examples
The sub-2-category of
Prof rep ↪ Prof on all representable profunctors is locally full.
The sub-2-category of the 2-category
of algebras for a T Alg l 2-monad and lax morphisms between them contains, as a locally full sub-2-category, the 2-category of algebras and pseudo morphisms (or of strict morphisms, if T Alg p is strict). T
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