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 . 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. 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.
Other articles related to "category":
... envelope construction associates to an arbitrary category a category together with a functor such that the image of every idempotent in splits in ... When applied to a preadditive category, the Karoubi envelope construction yields a pseudo-abelian category called the pseudo-abelian completion of ... To be precise, given a preadditive category we construct a pseudo-abelian category in the following way ...
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