By Emily Riehl

ISBN-10: 1107048451

ISBN-13: 9781107048454

This e-book develops summary homotopy conception from the explicit point of view with a selected specialise in examples. half I discusses competing views wherein one often first encounters homotopy (co)limits: both as derived functors definable whilst the ideal diagram different types admit a suitable version constitution, or via specific formulae that provide the fitting proposal in definite examples. Emily Riehl unifies those likely rival views and demonstrates that version constructions on diagram different types are beside the point. Homotopy (co)limits are defined to be a distinct case of weighted (co)limits, a foundational subject in enriched type thought. partially II, Riehl additional examines this subject, keeping apart express arguments from homotopical ones. half III treats the main ubiquitous axiomatic framework for homotopy concept - Quillen's version different types. the following, Riehl simplifies popular version specific lemmas and definitions by way of targeting susceptible factorization structures. half IV introduces quasi-categories and homotopy coherence.

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Categorical Homotopy Theory (New Mathematical Monographs) by Emily Riehl

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