What is a finitely related object, categorically?

Author's Department

Mathematics & Actuarial Science Department

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https://doi.org/10.1007/s10485-011-9250-7

Document Type

Research Article

Publication Title

Applied Categorical Structures

Publication Date

1-1-2013

doi

10.1007/s10485-011-9250-7

Abstract

The concept of a finitely related algebra, as opposed to the ones of finitely presentable and finitely generated ones, is not preserved under categorical equivalences. We propose a categorically well behaved approximation for it in the context of locally presentable categories, which turns out to be a natural counterpart to the (slightly reformulated) categorical definitions of finitely presentable and finitely generated objects. A stronger notion is also defined, which may be considered more natural in the restricted context of algebraic categories, as it corresponds to the classical one when the canonical theory is considered. Both concepts are equivalent to finite presentability when finite generation is added. © 2011 Springer Science+Business Media B.V.

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