Author : Emily Riehl
Release : 2022-02-10
Genre : Mathematics
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Book Rating : 194/5 ( reviews)

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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.