nLab
twisted module of homomorphisms

Let C be a dg-coalgebra, A a dg-algebra, N a left C-dg-comodule with coaction δ N:NCN, P a left A-dg-module with action m P:APP and τ:CA a twisting cochain. The twisted module of homomorphisms Hom τ(N,P) is a chain complex which as a graded module coincides with the ordinary module of homomorphisms of the underlying chain complex Hom(N,P), and with the differential d τ given by

d τ(f)=d(f)+m P(τf)δ N,d_\tau(f) = d(f) + m_P\circ(\tau\otimes f)\circ\delta_N,

where fHom(N,P).

Revised on March 15, 2009 22:32:33 by Zoran Škoda (195.37.209.180)