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A Whirlwind Tour of the World of $(\infty,1)$-categories

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arxiv 1303.4669 v3 pith:DKXL4KDR submitted 2013-03-19 math.CT

classification math.CT
keywords categorytheorycategorieshigherinftytheywhatalmost
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abstract

This introduction to higher category theory is intended to a give the reader an intuition for what $(\infty,1)$-categories are, when they are an appropriate tool, how they fit into the landscape of higher category, how concepts from ordinary category theory generalize to this new setting, and what uses people have put the theory to. It is a rough guide to a vast terrain, focuses on ideas and motivation, omits almost all proofs and technical details, and provides many references.

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  1. Simplicial sets in topology, category theory, and beyond

    math.AT 2024-11 unverdicted

    A clear, example-driven introduction to simplicial sets and their role as a bridge between topology and category theory.

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