The Monoidal Grothendieck Construction

My student Joe Moeller gave a talk at the MIT Categories Seminar today! People discussed his talk at the Category Theory Community Server, and if you join that you can see the discussion here:

https://categorytheory.zulipchat.com/#narrow/stream/229457-MIT-Categories.20Seminar/topic/April.2023.20-.20Joe.20Moeller’s.20talk

You can see his slides here, and watch a video of his talk here:

The monoidal Grothendieck construction

Abstract. The Grothendieck construction gives an equivalence between fibrations and indexed categories. We will begin with a review of the classical story. We will then lift this correspondence to two monoidal variants, a global version and a fibre-wise version. Under certain conditions these are equivalent, so one can transfer fibre-wise monoidal structures to the total category. We will give some examples demonstrating the utility of this construction in applied category theory and categorical algebra.

The talk is based on this paper:

• Joe Moeller and Christina Vasilakopoulou, Monoidal Grothendieck construction.

This, in turn, had its roots in our work on network models, a setup for the compositional design of networked systems:

• John Baez, John Foley, Joe Moeller and Blake Pollard, Network models.

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