Introduction to Homotopy Type Theory by Egbert Rijke
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.-
A Primer of Nonlinear Analysis
-
Complex Topological K-Theory
-
Mathematical Aspects of Quantum Field Theory
-
Enumerative Combinatorics: Volume 1
-
Hodge Theory and Complex Algebraic Geometry I: Volume 1
-
Random Graphs
-
Enumerative Combinatorics: Volume 2
-
Algebraic Number Theory
-
Spectral Theory and Differential Operators
-
An Introduction to the Theory of the Riemann Zeta-Function
-
Hardy Spaces
-
Gaussian Processes on Trees
-
Multidimensional Real Analysis I
-
Periodic Elliptic Partial Differential Operators
-
Higher Index Theory
-
A Course in Finite Group Representation Theory
-
Optimal Control and Geometry: Integrable Systems
-
The Theory of Fusion Systems
-
Derived Categories
-
Uniform Central Limit Theorems
-
Random Fragmentation and Coagulation Processes
-
Levy Processes and Stochastic Calculus
-
Holomorphic Dynamics
-
An Introduction to Invariants and Moduli
-
Quasiconformal Surgery in Holomorphic Dynamics
-
Martingales in Banach Spaces
-
Tolerance Graphs
-
An Outline of Ergodic Theory
-
Spectra of Discrete Structures
-
Analytic Combinatorics in Several Variables
-
Fourier Analysis and Partial Differential Equations
-
Riemannian Geometry
-
Representations of the Infinite Symmetric Group
-
Soliton Equations and their Algebro-Geometric Solutions: Volume 1, (1+1)-Dimensional Continuous Models
-
Local Cohomology
-
Multiplicative Number Theory I
-
Analysis in Integer and Fractional Dimensions
-
An Introduction to Nonlinear Analysis
-
Extremal Graph and Hypergraph Theory
-
The Bellman Function Technique in Harmonic Analysis
-
Explicit Brauer Induction
-
Random Walk: A Modern Introduction
-
Clifford Algebras and the Classical Groups
-
Wavelets
-
The Logarithmic Integral: Volume 2
Egbert Rijke is Postdoctoral Research Fellow at John Hopkins University and is a pioneering figure in homotopy type theory. As one of the co-authors of the influential book 'Homotopy Type Theory: Univalent Foundations for Mathematics' (2013), he has played a pivotal role in shaping the field. He is also a founder and lead developer of the agda-unimath library, which stands as the largest library of formalized mathematics written in the Agda proof assistant.
| SKU | Unavailable |
| ISBN 13 | 9781108844161 |
| ISBN 10 | 1108844162 |
| Title | Introduction to Homotopy Type Theory |
| Author | Egbert Rijke |
| Series | Cambridge Studies In Advanced Mathematics |
| Condition | Unavailable |
| Binding Type | Hardback |
| Publisher | Cambridge University Press |
| Year published | 2025-08-31 |
| Number of pages | 383 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |