Topology: A Categorical Approach by Tai-Danae Bradley, et al
Topology: A Categorical Approach - Table of Contents
0. Preliminaries
1. Examples and Constructions
2. Connectedness and Compactness
3. Limits of Sequences and Filters
4. Categorical Limits and Colimits
5. Adjunctions and the Compact-Open Topology
6. Paths, Loops, Cylinders, Suspensions
What You Will Learn in Topology: A Categorical Approach
"Topology: A Categorical Approach" by Tai-Danae Bradley, Tyler Bryson, and John Terilla is a modern introduction to "topology" through the lens of "category theory". It provides a fresh perspective on familiar concepts such as "compactness", "connectedness", and the Hausdorff condition by framing them in terms of functors, universal properties, and categorical constructions. The book is designed for graduate students or mathematically mature readers who want to deepen their understanding of topology with abstract, conceptual tools.
The text begins with the foundations of both category theory and classical topology, ensuring readers have the necessary background. It then explores key categorical concepts like limits, colimits, adjunctions, and mapping spaces, and shows how these tools illuminate traditional topological ideas. Classical results, including the fundamental groupoid and the Seifert–van Kampen theorem, are reinterpreted categorically, providing a unified and elegant viewpoint. Exercises throughout encourage readers to connect abstract theory to familiar examples, strengthening both intuition and technical skill.
Bradley et al.’s approach makes this book an excellent resource for those seeking a deeper, conceptual understanding of topology. By blending "category theory" and "topology", it equips readers to see beyond point-set methods, understand the relationships between spaces more abstractly, and develop tools that are widely applicable in modern mathematics, from algebraic topology to homotopy theory.
Book Details & Specifications
Title:
Topology: A Categorical Approach by Tai-Danae Bradley, et al
Publisher:
The MIT Press
Year:
2020
Pages:
166
Type:
PDF
Language:
English
ISBN-10 #:
0262539357
ISBN-13 #:
978-0262539357
License:
CC BY-NC-ND 2.0
Amazon:
Amazon
About the Author: Tai-Danae Bradley, Tyler Bryson and John Terilla
The author
Tai-Danae Bradley, Tyler Bryson and John Terilla
is a mathematician and educator known for her work in "category theory" and "topology". She earned her Ph.D. from the CUNY Graduate Center and created the popular blog "Math3ma", which explains advanced mathematical concepts in an accessible way to students and enthusiasts. She is the lead author of "Topology: A Categorical Approach", co-written with Tyler Bryson and John Terilla. This "graduate-level textbook" presents "point-set topology" using categorical tools such as universal properties, limits, and adjunctions, helping readers connect classical topology with modern mathematical structures. It is widely used for building deep theoretical understanding.
Read or Downloadable Topology: A Categorical Approach
Free Topology Books PDF | Curated Academic Directory