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{{Multiple issues|technical=June 2012|refimprove =June 2007|notability=June 2010}} | |||
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 (mathematics)|ring]], M,N,C be R-modules, and | |||
<math> \rho_M: M\rightarrow M\otimes C, \rho_N: N\rightarrow N\otimes C </math> | |||
be right C-[[comodule]]s. Then an R-linear map <math> f:M\rightarrow N</math> is called a '''(right) comodule morphism''', or '''(right) C-colinear''', if | |||
<math> \rho_N \circ f = (f \otimes 1) \circ \rho_M </math> | |||
==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 | |||
[[Category:Coalgebras]] | |||
{{algebra-stub}} | |||
Latest revision as of 01:33, 9 January 2013
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
be right C-comodules. Then an R-linear map is called a (right) comodule morphism, or (right) C-colinear, if
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