Discrete and concrete objects
For a functor we say that it has codiscrete objects if it has a full and faithful right adjoint .
This is for instance the case for the global section geometric morphism of a local topos .
In this situation, we say that a concrete object is one for which the -unit of an adjunction is a monomorphism.
If is a sheaf topos, this is called a concrete sheaf.
If is a cohesive (∞,1)-topos then this is called a concrete (∞,1)-sheaf or the like.
The dual notion is that of a co-concrete object.
is a faithful functor on morphisms whose codomain is concrete.
graded differential cohesion
Revised on February 20, 2013 10:37:24
by Urs Schreiber