The principal topics are as follows: Basic Homotopy; H-spaces and co-H-spaces; fibrations and cofibrations; exact sequences of homotopy sets, actions, and coactions; homotopy pushouts …

Homotopy type theory offers a new “univalent” foundation of mathematics, in which a central role is played by Voevodsky’s univalence axiom and higher inductive types.

2020年1月23日 · The Handbook of Homotopy Theory provides a panoramic view of an active area in mathematics that is currently seeing dramatic solutions to long-standing open …

2022年12月21日 · This is an introductory textbook to univalent mathematics and homotopy type theory, a mathematical foundation that takes advantage of the structural nature of …

The first six chapters describe the essential ideas of homotopy theory: homotopy groups, the classical theorems, the exact homotopy sequence, fibre-spaces, the Hopf invariant, and the …

Nilpotence and Periodicity in Stable Homotopy Theory describes some major advances made in algebraic topology in recent years, centering on the nilpotence and periodicity theorems, which …

2011年7月25日 · This is a book in pure mathematics dealing with homotopy theory, one of the main branches of algebraic topology. The principal topics are as follows: • Basic Homotopy; • …

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 …

This book gives a general outlook on homotopy theory; fundamental concepts, such as homotopy groups and spectral sequences, are developed from a few axioms and are thus available in a …