nLab
hom-category

Idea

Recall that in a category CC, each pair of objects xx and yy determines a set C(x,y)C(x,y), the hom-set of xx and yy. In a 22-category BB, each pair of objects determines a category B(x,y)B(x,y). This category is the hom-category of xx and yy.

As a 22-category is enriched over Cat, a hom-category is a special case of a hom-object. But the hom-category makes sense also for the weakly enriched concept of bicategory.

Revised on July 28, 2011 15:21:06 by Urs Schreiber (82.113.99.20)