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Polynomials via fibrations

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If you have a question about this talk, please contact Jamie Vicary.

Polynomials in category theory represent datatypes which, like polynomial functions, can be expressed using sums and products. Extending this analogy, I will characterize the category of polynomials in terms of indexed sums and products for fibrations. This category arises from a distributive law between the pseudomonad ‘freely adding’ indexed sums to a fibration, and its dual adding indexed products. I will also relate this perspective to the structure of categorical models of type theory with dependent sum and product types.

This talk is part of the Theoretical computer science seminar series.

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