Topological half-exact functor
In mathematics, a topological half-exact functor F is a functor from a fixed topological category to an abelian category that has a following property: for each sequence of spaces, of the form:
where C denotes a mapping cone, the sequence:
is exact. If F is a contravariant functor, it is half-exact if for each sequence of spaces as above,
the sequence F → F → F is exact.
Homology is an example of a half-exact functor, and
cohomology are examples of contravariant half-exact functors.
If B is any fibrant topological space, the functor F= is half-exact.
