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Basic Concepts of Enriched Category Theory

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Sets appear everywhere in category theory. The definitions of locally small categories, limits and colimits, and many results including the Yoneda lemma are given in terms of sets and maps between them. The idea of enriched category theory is to systematically replace sets and functions in these results with objects and morphisms from another category. In my talk I will define and discuss some of the basic notions of enriched category theory and prove an enriched version of the Yoneda lemma. I will also discuss some examples of how some other mathematical objects can be viewed as enriched categories.

This talk is part of the Junior Category Theory Seminar series.

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