Pseudo-abelian Category

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 CategoryExamples, 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 ...

Famous quotes containing the word category:

    The truth is, no matter how trying they become, babies two and under don’t have the ability to make moral choices, so they can’t be “bad.” That category only exists in the adult mind.
    Anne Cassidy (20th century)