Book Volume 364 2014

Axiomatic Method and Category Theory

Authors:

ISBN: 978-3-319-00403-7 (Print) 978-3-319-00404-4 (Online)

Table of contents (10 chapters)

  1. Front Matter

    Pages i-xi

  2. No Access

    Chapter

    Pages 1-12

    Introduction

  3. A Brief History of the Axiomatic Method

    1. Front Matter

      Pages 13-14

    2. No Access

      Chapter

      Pages 15-37

      Euclid: Doing and Showing

    3. No Access

      Chapter

      Pages 39-72

      Hilbert: Making It Formal

    4. No Access

      Chapter

      Pages 73-97

      Formal Axiomatic Method and the Twentieth Century Mathematics

    5. No Access

      Chapter

      Pages 99-143

      Lawvere: Pursuit of Objectivity

    6. Back Matter

      Pages 145-146

  4. Identity and Categorification

    1. Front Matter

      Pages 147-147

    2. No Access

      Chapter

      Pages 149-173

      Identity in Classical and Constructive Mathematics

    3. No Access

      Chapter

      Pages 175-209

      Identity Through Change, Category Theory and Homotopy Theory

    4. Back Matter

      Pages 211-212

  5. Subjective Intuitions and Objective Structures

    1. Front Matter

      Pages 213-213

    2. No Access

      Chapter

      Pages 215-234

      How Mathematical Concepts Get Their Bodies

    3. No Access

      Chapter

      Pages 235-263

      Categories Versus Structures

    4. No Access

      Chapter

      Pages 265-272

      New Axiomatic Method (Instead of Conclusion)

  6. Back Matter

    Pages 273-285