An
-category
is a category equipped with an
-module structure on each hom set such that the composition is
-bilinear. More precisely, let us assume for instance that we are given a commutative ring
with identity. Then a small
-category-or equivalently an
-algebroid- will be defined as a category enriched in the monoidal category of
-modules, with respect to the monoidal structure of tensor
product. This means simply that for all objects
of
, the set
is given the structure of an
-module, and composition
is
-bilinear, or is a morphism of
-modules
.
As of this snapshot date, this entry was owned by bci1.