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Introduction to Homotopy Type Theory
Hardcover
Series: Cambridge Studies in Advanced Mathematics, Book 219
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ISBN10: 1108844162
ISBN13: 9781108844161
Publisher: Cambridge University Press
Published: Nov 6 2025
Pages: 386
Weight: 1.51
Height: 0.88 Width: 6.00 Depth: 9.00
Language: English
ISBN13: 9781108844161
Publisher: Cambridge University Press
Published: Nov 6 2025
Pages: 386
Weight: 1.51
Height: 0.88 Width: 6.00 Depth: 9.00
Language: English
This up-to-date introduction to type theory and homotopy type theory will be essential reading for advanced undergraduate and graduate students interested in the foundations and formalization of mathematics. The book begins with a thorough and self-contained introduction to dependent type theory. No prior knowledge of type theory is required. The second part gradually introduces the key concepts of homotopy type theory: equivalences, the fundamental theorem of identity types, truncation levels, and the univalence axiom. This prepares the reader to study a variety of subjects from a univalent point of view, including sets, groups, combinatorics, and well-founded trees. The final part introduces the idea of higher inductive type by discussing the circle and its universal cover. Each part is structured into bite-size chapters, each the length of a lecture, and over 200 exercises provide ample practice material.
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