The Simplex Category: Simplicial Sets

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Description

This lecture introduces the combinatorics of the simplex category, a category that allows defining homotopy theory equivalent to that of topological spaces. It covers the definition of the simplex category, the concept of coface and codegeneracy maps, and the cosimplicial identities. The lecture also explores the functor categories Fun(A,C) and Fun(AOP, C) as categories of cosimplicial and simplicial objects in C, respectively.

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https://mediaspace.epfl.ch/media/0_9ev2ib77

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A proof is sufficient evidence or a sufficient argument for the truth of a proposition. The concept applies in a variety of disciplines, with both the nature of the evidence or justification and the criteria for sufficiency being area-dependent. In the area of oral and written communication such as conversation, dialog, rhetoric, etc., a proof is a persuasive perlocutionary speech act, which demonstrates the truth of a proposition.