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

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.

For more information, contact luca.spada at gmail.com