Discrete and concrete objects
For a functor we say that it has codiscrete objects if it has a full and faithful right adjoint .
An object in the essential image of is called a codiscrete object.
This is for instance the case for the global section geometric morphism of a local topos .
If one thinks of as a category of spaces, then the codiscrete objects are called codiscrete spaces.
The dual notion is that of discrete objects.
is a faithful functor on morphisms whose codomain is concrete.
If has a terminal object that is preserved by , then has concrete objects.
This is (Shulman, theorem 1).
This is (Shulman, theorem 2).
graded differential cohesion
Revised on January 5, 2013 21:56:47
by Urs Schreiber