Given a category
and a ring
, one can construct an
algebra
as follows. Let
be the set of
all formal finite linear combinations of the form
where the coefficients
Two instances of this construction are worth noting. If
is a group,
we may regard
as a category with one object. Then this construction
gives us the group algebra of
. If
is a partially ordered set,
we may view
as a category with at most one morphism between any
two objects. Then this construction provides us with the incidence
algebra of
.
As of this snapshot date, this entry was owned by rspuzio.