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Institute for Logic, Language and Computation

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9 October 2013, Algebra|Coalgebra Seminar, Luca Spada (ILLLC and University of Salerno)

Speaker: Luca Spada (ILLLC and University of Salerno)
Title: Two isomorphism criteria for directed colimits
Date: Wednesday 9 October 2013
Time: 16:00-18:00
Location: ILLC seminar room (F1.15), Science Park 107, Amsterdam

Using the general notions of finite presentable and finitely generated object introduced by Gabriel and Ulmer
in 1971, we prove that, in any category, two sequences of finitely presentable objects and morphisms (or two sequences of finitely generated objects and monomorphisms) have isomorphic colimits (=direct limits) if, and only if, they are confluent. The latter means that the two given sequences can be connected by a back-and-forth sequence of morphisms that is cofinal on each side, and commutes with the sequences at each finite stage. We illustrate
the criterion by applying the abstract results to varieties (=equationally definable classes) of algebras, and mentioning applications to non-equational examples.

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Please note that this newsitem has been archived, and may contain outdated information or links.