induced comodule

Given a commutative unital ring k and a morphism DC of k-coalgebras, one can consider the dualized notion of induced module, using the cotensor product instead of tensor product.

If D is flat as a k-module (e.g. k is a field), and N a left D- right C-bicomodule, then the cotensor product NM is a D-subcomodule of N kM. In particular, under the flatness assumption, if π:DC is a surjection of coalgebras then D is a left D- right C-bicomodule via Δ D and (idπ)Δ D respectively, hence Ind C D:=D C is a functor from left C- to left D-comodules called the induction functor for left comodules from C to D.

One can consider this construction more generally for corings.

Created on November 12, 2012 02:37:54 by Zoran Škoda (