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Showing posts from October 3, 2021

### Forms vs monoidal categories

Below is a summary of the talk given at the Séminaire Itinérant de Catégories  (8 October 2021), prepared before the talk.  The talk is mainly based on Zurab Janelidze's joint work in progress with Francois van Niekerk, as well as his earlier work on forms with former collaborators. The talk assumes that the listener is familiar with basic ideas and concepts of category theory found in Categories for the Working Mathematician by Saunders Mac Lane (in particular, Chapters I, VII and VIII), as well as with the notions of factorization system and Grothendieck fibration. 1. Biproducts, products, sums and monoidal categories The goal of this talk is to explain the following diagram: The notion of an abelian category brings together various important categories of abstract mathematics, such as the categories of modules, which includes the category of vector spaces as well as the category of abelian groups. In an abelian category, the monoidal structure of product and the monoidal stru