Download e-book for iPad: Categorical Homotopy Theory (New Mathematical Monographs) by Emily Riehl

By Emily Riehl

ISBN-10: 1107048451

ISBN-13: 9781107048454

This ebook develops summary homotopy concept from the specific viewpoint with a specific specialise in examples. half I discusses competing views wherein one in general first encounters homotopy (co)limits: both as derived functors definable whilst the correct diagram different types admit a appropriate version constitution, or via specific formulae that provide the precise thought in sure 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 class idea. partially II, Riehl additional examines this subject, keeping apart express arguments from homotopical ones. half III treats the main ubiquitous axiomatic framework for homotopy conception - Quillen's version different types. the following, Riehl simplifies widely used version specific lemmas and definitions by means of targeting vulnerable 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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