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In mathematics, specifically in category theory, a pseudo-abelian category is a category that is preadditive and is such that every idempotent has a kernel .〔Artin, 1972, p. 413.〕 Recall that an idempotent morphism is an endomorphism of an object with the property that . Elementary considerations show that every idempotent then has a cokernel.〔Lars Brünjes, Forms of Fermat equations and their zeta functions, Appendix A〕 The pseudo-abelian condition is stronger than preadditivity, but it is weaker than the requirement that every morphism have a kernel and cokernel, as is true for abelian categories. Synonyms in the literature for pseudo-abelian include pseudoabelian and Karoubian. == Examples == Any abelian category, in particular the category Ab of abelian groups, is pseudo-abelian. Indeed, in an abelian category, ''every'' morphism has a kernel. The category of associative rngs (not rings!) together with multiplicative morphisms is pseudo-abelian. A more complicated example is the category of Chow motives. The construction of Chow motives uses the pseudo-abelian completion described below. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Pseudo-abelian category」の詳細全文を読む スポンサード リンク
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