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

By Emily Riehl

This ebook develops summary homotopy concept from the specific viewpoint with a selected specialise in examples. half I discusses competing views wherein one commonly first encounters homotopy (co)limits: both as derived functors definable whilst the best diagram different types admit a appropriate version constitution, or via specific formulae that supply the precise proposal in definite examples. Emily Riehl unifies those possible rival views and demonstrates that version buildings on diagram different types are inappropriate. Homotopy (co)limits are defined to be a different case of weighted (co)limits, a foundational subject in enriched classification idea. partly II, Riehl extra 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 typical version specific lemmas and definitions through targeting vulnerable factorization platforms. half IV introduces quasi-categories and homotopy coherence.

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