Let be a functor from the category of topological spaces to some category . Then is called homotopy invariant if for any two homotopic maps between topological spaces and the morphisms and in induced by are identical.
Suppose is a homotopy invariant functor, and and are homotopy equivalent topological spaces. Then there are continuous maps and such that and (i.e. and are homotopic to the identity maps on and , respectively). Assume that is a covariant functor. Then the homotopy invariance of implies
An important example of a homotopy invariant functor is the fundamental group ; here is the category of groups.
|Date of creation||2013-03-22 14:24:51|
|Last modified on||2013-03-22 14:24:51|
|Last modified by||pbruin (1001)|