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projective cover : ウィキペディア英語版
projective cover
In the branch of abstract mathematics called category theory, a projective cover of an object ''X'' is in a sense the best approximation of ''X'' by a projective object ''P''. Projective covers are the dual of injective envelopes.
== Definition ==

Let \mathcal be a category and ''X'' an object in \mathcal. A projective cover is a pair (''P'',''p''), with ''P'' a projective object in \mathcal and ''p'' a superfluous epimorphism in Hom(''P'', ''X'').
If ''R'' is a ring, then in the category of ''R''-modules, a superfluous epimorphism is then an epimorphism p : P \to X such that the kernel of ''p'' is a superfluous submodule of ''P''.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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