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**.

Read more about Pseudo-abelian Category: Examples, Pseudo-abelian Completion

### Other articles related to "category":

**Pseudo-abelian Category**- Pseudo-abelian Completion

... 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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