Stable homotopy theory
For locally small categories
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 enriched categories
For a category enriched over a category , the “hom-set” is an object of , the hom-object.
For internal categories
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 identitfy morphisms with global objects of and form as above.
Revised on December 21, 2011 19:19:02
by Urs Schreiber