Categorical models of dependent types

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• Ian Orton (University of Cambridge)
• Friday 22 January 2016, 11:00-12:00
• Rainbow Room (FS07), Computer Laboratory.

If you have a question about this talk, please contact Ian Orton.

I will run through the basics of how dependent types are modelled inside a category, including how to construct dependent sums and products, and how to represent substitution. I will then discuss the coherence issues relating to substitution and how these can be resolved using a category with families (CwF) or similar construction (e.g. comprehension categories, categories with attributes etc).

Covering:

• Dependent types as fibrations
• Dependent sum/product as adjoints to the pullback functor
• Substitution via pullback and its problems
• Fixing those problems with categories with families (CwFs)

Prerequisites:

• Basic category theory (functors and pullbacks)
• Basic knowledge of dependent types

This talk is part of the Logic & Semantics for Dummies series.

This talk is included in these lists:

• Logic & Semantics for Dummies
• Rainbow Room (FS07), Computer Laboratory
• tcw57’s list
• yk373's list

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