nLab
codiscrete object
Contents
Context
Discrete and concrete objects
Category Theory
Contents
Definition
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.
Examples
Properties
Proposition
If has a terminal object that is preserved by , then has concrete objects.
This is (Shulman, theorem 1).
This is (Shulman, theorem 2).
cohesion
infinitesimal cohesion
tangent cohesion
differential cohesion
graded differential cohesion
singular cohesion
References
Last revised on August 25, 2021 at 17:30:48.
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