twisted module of homomorphisms

Let $C$ be a dg-coalgebra, $A$ a dg-algebra, $N$ a left $C$-dg-comodule with coaction ${\delta}_{N}:N\to C\otimes N$, $P$ a left $A$-dg-module with action ${m}_{P}:A\otimes P\to P$ and $\tau :C\to A$ a twisting cochain. The **twisted module of homomorphisms** ${\mathrm{Hom}}_{\tau}(N,P)$ is a chain complex which as a graded module coincides with the ordinary module of homomorphisms of the underlying chain complex $\mathrm{Hom}(N,P)$, and with the differential ${d}_{\tau}$ given by

$${d}_{\tau}(f)=d(f)+{m}_{P}\circ (\tau \otimes f)\circ {\delta}_{N},$$

where $f\in \mathrm{Hom}(N,P)$.

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