MIT Category Theory Seminar 2019/10/10
©Spifong
Title: Supplying Bells and Whistles in Symmetric Monoidal Categories
Abstract: Morphisms in a symmetric monoidal category can be depicted using string diagrams; this is a celebrated fact that underpins much of applied catgeory theory. It often happens, however, that one wishes to use special, additional icons in a string diagram language; more formally, this means every object is equipped with additional algebraic structure. For example, in a hypergraph category each object is equipped with a notion of wiring, or in a category with products each object has a diagonal map. In these cases, the minimal structure required for a nice string diagram language is a simple compatibility condition between the algebraic structures on each object and the monoidal product. If this condition holds, we say that the category supplies the structure.
In this talk I'll give some examples of supply, and outline a few theorems that show the compatibility condition is really what is necessary for nice diagrams. The material will form an accessible introduction to my paper with David of the above title.
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