Locally discrete bicategories #
C can be promoted to a strict bicategory
LocallyDiscrete C. The objects and the
LocallyDiscrete C are the same as the objects and the morphisms, respectively,
C, and the 2-morphisms in
LocallyDiscrete C are the equalities between 1-morphisms. In
other words, the category consisting of the 1-morphisms between each pair of objects
LocallyDiscrete C is defined as the discrete category associated with the type
X ⟶ Y.
The locally discrete bicategory on a category is a bicategory in which the objects and the 1-morphisms are the same as those in the underlying category, and the 2-morphisms are the equalities between 1-morphisms.
B is a strict bicategory and
I is a (1-)category, any functor (of 1-categories)
I ⥤ B can
be promoted to an oplax functor from
LocallyDiscrete I to