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COLINEA

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Colinea might refer to

Colinea might be related to
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 * * * {\displaystyle \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 * → * N * * * {\displaystyle f:M\rightarrow N} * is called a (right) comodule morphism, or (right) C-colinear, if * * * * * ρ * * N * * * ∘ * f * = * ( * f * ⊗ * 1 * ) * ∘ * * ρ * * M * * * * * {\displaystyle \rho _{N}\circ f=(f\otimes 1)\circ \rho _{M}}

Colinea might be related to

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
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* {\displaystyle \rho _{M}:M\rightarrow M\otimes C,\rho _{N}:N\rightarrow N\otimes C}
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* be right C-comodules. Then an R-linear map
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* {\displaystyle f:M\rightarrow N}
* is called a (right) comodule morphism, or (right) C-colinear, if
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* {\displaystyle \rho _{N}\circ f=(f\otimes 1)\circ \rho _{M}}

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