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

ρ M : M → M ⊗ C , ρ N : N → N ⊗ C

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

ρ N ∘ f = ( f ⊗ 1 ) ∘ ρ M