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Download Categorical Homotopy Theory (New Mathematical Monographs) by Emily Riehl PDF

By Emily Riehl

This publication develops summary homotopy idea from the explicit point of view with a specific specialize in examples. half I discusses competing views through which one usually first encounters homotopy (co)limits: both as derived functors definable while definitely the right diagram different types admit a suitable version constitution, or via specific formulae that supply the best thought in yes examples. Emily Riehl unifies those doubtless rival views and demonstrates that version buildings on diagram different types are beside the point. Homotopy (co)limits are defined to be a different case of weighted (co)limits, a foundational subject in enriched type conception. 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. right here, Riehl simplifies customary version specific lemmas and definitions by way of concentrating on vulnerable factorization structures. half IV introduces quasi-categories and homotopy coherence.

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