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Displayed categories

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Displayed categories formalize the activity of building new categories from old ones by considering `objects with structure’. They also allow one to give a simple definition of fibration without referring to equality of objects. In my talk, I develop some `displayed category theory’. I then give some use cases: first, the construction of an equivalence of categories between cwf structures and split type structures, and second, a proof of the Structure Identity Principle using displayed category theory. Afterwards I discuss the definition of fibrations in terms of displayed categories. This is joint work with Peter Lumsdaine.

This talk is part of the Category Theory Seminar series.

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