Elements of ∞-Category Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elements of ∞-Category Theory write by Emily Riehl. This book was released on 2022-02-10. Elements of ∞-Category Theory available in PDF, EPUB and Kindle. The language of ∞-categories provides an insightful new way of expressing many results in higher-dimensional mathematics but can be challenging for the uninitiated. To explain what exactly an ∞-category is requires various technical models, raising the question of how they might be compared. To overcome this, a model-independent approach is desired, so that theorems proven with any model would apply to them all. This text develops the theory of ∞-categories from first principles in a model-independent fashion using the axiomatic framework of an ∞-cosmos, the universe in which ∞-categories live as objects. An ∞-cosmos is a fertile setting for the formal category theory of ∞-categories, and in this way the foundational proofs in ∞-category theory closely resemble the classical foundations of ordinary category theory. Equipped with exercises and appendices with background material, this first introduction is meant for students and researchers who have a strong foundation in classical 1-category theory.
Category Theory in Context
Category Theory in Context - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Category Theory in Context write by Emily Riehl. This book was released on 2017-03-09. Category Theory in Context available in PDF, EPUB and Kindle. Introduction to concepts of category theory — categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads — revisits a broad range of mathematical examples from the categorical perspective. 2016 edition.
Basic Category Theory
Basic Category Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Basic Category Theory write by Tom Leinster. This book was released on 2014-07-24. Basic Category Theory available in PDF, EPUB and Kindle. A short introduction ideal for students learning category theory for the first time.
Categorical Homotopy Theory
Categorical Homotopy Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Categorical Homotopy Theory write by Emily Riehl. This book was released on 2014-05-26. Categorical Homotopy Theory available in PDF, EPUB and Kindle. 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.
Basic Concepts of Enriched Category Theory
Basic Concepts of Enriched Category Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Basic Concepts of Enriched Category Theory write by Gregory Maxwell Kelly. This book was released on 1982-02-18. Basic Concepts of Enriched Category Theory available in PDF, EPUB and Kindle.
