# Colinear map

Colinear map

In coalgebra theory, the notion of colinear map is dual to the notion for linear map of vector space, or more generally, for morphism between R-module. Specifically, let R be a ring, M,N,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