CategoryTheory / News: Recent posts

Any Z – module homomorphism f from A to B defines natural transformation from Hom(-,A) to Hom(-,B) functor. The same is true for Hom(A,-), Ext(-,A), Ext(A,-) and also Tor and tensor product functors. New release contains calculation of these natural transformations.

Prospects:

1) Development of simplicial category support.
2) Development of homotopic category support.

Objects of homotopic category will include homotopy invariants and relations between them. The invariants include homotopic groups, (co)homology, cobordisms, K – theory, etc. Relations include characteristic class, Gurevich homomorphism, natural transformations between different (co)homology theories.