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The Fundamental Theorem of Category Theory

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If you have a question about this talk, please contact Guilherme Lima de Carvalho e Silva.

This talk will consist of three parts. In the first part I will formulate and proof the ‘fundamental theorem’ as a form of generalized tensor-hom adjunction. In the second part I will justify why it is ‘fundamental’ by discussing some of its important applications. This will involve the adjunction of geometric realization of simplicial sets in algebraic topology, the equivalence of sheaves on a topological space X and étale spaces over X and applications in the theory of geometric morphisms. In the third part I will take the representation theoretic point of view on functors and explain, why the fundamental theorem is indeed a tensor-hom adjunction in this generalized sense.

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

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