hom-set, hom-object, internal hom, exponential object, derived hom-space
loop space object, free loop space object, derived loop space
Given objects and in a locally small category, the hom-set is the collection of all morphisms from to . In a closed category, the hom-set may also be called the external hom to distinguish it from the internal hom.
For a category enriched over a category , the “hom-set” is an object of , the hom-object.
For an internal category, the generalized objects of are morphisms and , and the “hom-set” becomes the pullback in
In particular, in a category with a terminal generator , we may identify morphisms with global objects of and form as above.
hom-set, hom-group
Textbook accounts:
Last revised on May 20, 2023 at 08:51:53. See the history of this page for a list of all contributions to it.