Colinear map

In coalgebra theory, the notion of a colinear map is dual to the notion of a linear map between vector spaces, or more generally, of a homomorphism between R-modules. Specifically, let R be a ring, M, N, and C be R-modules, and

\rho _{M}:M\rightarrow M\otimes C,\ \rho _{N}:N\rightarrow N\otimes C

be right C-comodules. Then an R-linear map $f:M\rightarrow N$ is called a (right) comodule morphism, or (right) C-colinear, if

\rho _{N}\circ f=(f\otimes 1)\circ \rho _{M}.

References

Khaled AL-Takhman, Equivalences of Comodule Categories for Coalgebras over Rings, J. Pure Appl. Algebra,.V. 173, Issue: 3, September 7, 2002, pp. 245–271