Categorical Homotopy Theory

Nonfiction, Science & Nature, Mathematics, Topology, Geometry
Cover of the book Categorical Homotopy Theory by Emily Riehl, Cambridge University Press
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Emily Riehl ISBN: 9781139949460
Publisher: Cambridge University Press Publication: May 26, 2014
Imprint: Cambridge University Press Language: English
Author: Emily Riehl
ISBN: 9781139949460
Publisher: Cambridge University Press
Publication: May 26, 2014
Imprint: Cambridge University Press
Language: English

This book develops abstract homotopy theory from the categorical perspective with a particular focus on examples. Part I discusses two competing perspectives by which one typically first encounters homotopy (co)limits: either as derived functors definable when the appropriate diagram categories admit a compatible model structure, or through particular formulae that give the right notion in certain examples. Emily Riehl unifies these seemingly rival perspectives and demonstrates that model structures on diagram categories are irrelevant. Homotopy (co)limits are explained to be a special case of weighted (co)limits, a foundational topic in enriched category theory. In Part II, Riehl further examines this topic, separating categorical arguments from homotopical ones. Part III treats the most ubiquitous axiomatic framework for homotopy theory - Quillen's model categories. Here, Riehl simplifies familiar model categorical lemmas and definitions by focusing on weak factorization systems. Part IV introduces quasi-categories and homotopy coherence.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

This book develops abstract homotopy theory from the categorical perspective with a particular focus on examples. Part I discusses two competing perspectives by which one typically first encounters homotopy (co)limits: either as derived functors definable when the appropriate diagram categories admit a compatible model structure, or through particular formulae that give the right notion in certain examples. Emily Riehl unifies these seemingly rival perspectives and demonstrates that model structures on diagram categories are irrelevant. Homotopy (co)limits are explained to be a special case of weighted (co)limits, a foundational topic in enriched category theory. In Part II, Riehl further examines this topic, separating categorical arguments from homotopical ones. Part III treats the most ubiquitous axiomatic framework for homotopy theory - Quillen's model categories. Here, Riehl simplifies familiar model categorical lemmas and definitions by focusing on weak factorization systems. Part IV introduces quasi-categories and homotopy coherence.

More books from Cambridge University Press

Cover of the book The New Emily Dickinson Studies by Emily Riehl
Cover of the book The First Part of King Henry VI by Emily Riehl
Cover of the book Gaseous Radiation Detectors by Emily Riehl
Cover of the book The Cambridge Habermas Lexicon by Emily Riehl
Cover of the book Patents and Innovation in Mainland China and Hong Kong by Emily Riehl
Cover of the book Time and Environmental Law by Emily Riehl
Cover of the book People with Disabilities by Emily Riehl
Cover of the book The Material Life of Roman Slaves by Emily Riehl
Cover of the book Thermoplasmonics by Emily Riehl
Cover of the book Max Horkheimer and the Foundations of the Frankfurt School by Emily Riehl
Cover of the book Lifetime Disadvantage, Discrimination and the Gendered Workforce by Emily Riehl
Cover of the book The Language of Service Encounters by Emily Riehl
Cover of the book Enlightenment and the Creation of German Catholicism by Emily Riehl
Cover of the book Conflict-Related Violence Against Women by Emily Riehl
Cover of the book Oil and Governance by Emily Riehl
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy