The core of a category #
The core of a category
C is the (non-full) subcategory of
C consisting of all objects,
and all isomorphisms. We construct it as a
F from a groupoid
C factors through
but this is not functorial with respect to
A functor from a groupoid to a category C factors through the core of C.
We can functorially associate to any functor from a groupoid to the core of a category
a functor from the groupoid to
C, simply by composing with the embedding
Core C ⥤ C.