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A First Course in Category Theory

  • Textbook
  • © 2023

Overview

Authors:
  1. Ana Agore

    1. Institute of Mathematics, Romanian Academy, Bucharest, Romania

  • Perfectly suited for a first introductory course in category theory
  • Thoroughly covers fundamentals concepts
  • Includes concrete examples from familiar mathematics

Part of the book series: Universitext (UTX)

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About this book



This textbook provides a first introduction to category theory, a powerful framework and tool for understanding mathematical structures. Designed for students with no previous knowledge of the subject, this book offers a gentle approach to mastering its fundamental principles.


Unlike traditional category theory books, which can often be overwhelming for beginners, this book has been carefully crafted to offer a clear and concise introduction to the subject. It covers all the essential topics, including categories, functors, natural transformations, duality, equivalence, (co)limits, and adjunctions. Abundant fully-worked examples guide readers in understanding the core concepts, while complete proofs and instructive exercises reinforce comprehension and promote self-study. The author also provides background material and references, making the book suitable for those with a basic understanding of groups, rings, modules, topological spaces, and set theory.


Based on the author's course at the Vrije Universiteit Brussel, the book is perfectly suited for classroom use in a first introductory course in category theory. Its clear and concise style, coupled with its detailed coverage of key concepts, makes it equally suited for self-study.

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Categories and Functors

    • Ana Agore
    Pages 1-81

  3. Limits and Colimits

    • Ana Agore
    Pages 83-151

  4. Adjoint Functors

    • Ana Agore
    Pages 153-250

  5. Solutions to Selected Exercises

    • Ana Agore
    Pages 251-275

  6. Back Matter

    Pages 277-284
    Download chapter PDF
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Reviews

“This book is a basic introduction to category theory at an undergraduate level, aimed at facilitating and making as accessible as possible the learning of the main notions, problems, ideas and techniques of the theory to any student or researcher without background in the field. … Each chapter is accompanied by a final section of recapitulation exercises, many of which are solved at the end of the book, and which offer a good test for students.” (Federico Giovanni Infusino, Mathematical Reviews, October, 2024)

Authors and Affiliations

  • Institute of Mathematics, Romanian Academy, Bucharest, Romania

    Ana Agore

About the author

Ana Agore is Senior Researcher at the Institute of Mathematics of the Romanian Academy, Romania, and Guest Professor at Vrije Universiteit Brussel, Belgium. Her research covers topics in quantum groups and Hopf algebras, non-associative algebras, group theory and category theory. 

Accessibility Information

PDF accessibility summary

This PDF does not fully comply with PDF/UA standards, but does feature limited screen reader support, described non-text content (images, graphs), bookmarks for easy navigation and searchable, selectable text. Users of assistive technologies may experience difficulty navigating or interpreting content in this document. We recognize the importance of accessibility, and we welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us at [email protected].

EPUB accessibility summary

This ebook is designed with accessibility in mind, aiming to meet the ePub Accessibility 1.0 AA and WCAG 2.0 Level AA standards. Its features include described images and other non-text content, screenreader-friendly navigation and accessible math. Math is represented either as MathML, LaTeX or in images. If math is represented as image, Alt Text might not be present. We recognize the importance of accessibility, and we welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us at [email protected].

Bibliographic Information

  • Book Title: A First Course in Category Theory

  • Authors: Ana Agore

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-3-031-42899-9

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023

  • Softcover ISBN: 978-3-031-42898-2Published: 13 December 2023

  • eBook ISBN: 978-3-031-42899-9Published: 12 December 2023

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: XIV, 284

  • Topics: Category Theory, Homological Algebra

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