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Locally graded categories

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If you have a question about this talk, please contact Tamara von Glehn.

This talk has two aims.

Firstly to introduce the notion of locally graded category, which generalizes that of enriched category, actegory and op-actegory. And the notion of locally indexed category, which is equivalent in the cartesian case to locally graded category.

Secondly to use these notions to give a cleaner categorical semantics of call-by-push-value (a form of lambda-calculus with computational effects) than the one I previously presented. It’s an improvement because it allows an apparently complicated equivalence (between two notions of adjunction) to be decomposed into simple parts.

This all builds on work of Wood, Egger-Mogelberg-Simpson and Mellies.

I will begin the talk with two pieces of background, that may be of independent interest:

(i) terminology for dealing with size issues

(ii) the notions of left module, right module and bimodule (aka profunctor) and some properties.

This talk is part of the Category Theory Seminar series.

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