On Wednesday, 12 November, I will give a talk in Algebra|Coalgebra seminar at the ILLC in Amsterdam. There I will define the notion of enriched presheaves and define a Morita duality, which I argue to be suitable for the construction of logics for coalgebras in enriched categories.

Title: Morita-Duality for Categories of Enriched Presheaves, The Case of Abelian Groups

Abstract: Morita Duality, due to Kiiti Morita 1958, describes a dually adjoint pair of functors
between the categories of left and right modules over a given pair of rings, which restricted
to certain subcategories yields a dual equivalence. In their categorification modules are
conceived as Ab-functors from a one-element category enriched over abelian groups to the
category of abelian groups. I will introduce the slightly more general notion of functors
enriched over arbitrary symmetric monoidal closed categories and in particular develop the
definition of a presheaf enriched over such categories. For the latter I will give the
definition of Morita duality in consistency with the Morita duality for modules. I show that
the initial and final sequence in the categories of Ab-presheaves correspond under Morita
duality, which motivates its use for coalgebraic logic in enriched categories.