nLab Handbook of Categorical Algebra

This entry is to record the monograph

• Francis Borceux,

  Handbook of Categorical Algebra

  • Vol. 1:

    Basic Category Theory

    doi:10.1017/CBO9780511525858

  • Vol. 2:

    Categories and Structures

    doi:10.1017/CBO9780511525865

  • Vol. 3:

    Categories of Sheaves

    doi:10.1017/CBO9780511525872

  Encyclopedia of Mathematics and its Applications 50

  Cambridge University Press (1994)

on category theory, categorical algebra and topos theory.

Book review:

• Peter Johnstone, Bull. London Math. Soc. 28:4, 440-442 (doi:10.1112/blms/28.4.440)

Contents

Vol. 1: Basic Category Theory

Preface; Introduction; 1. The language of categories; 2. Limits; 3. Adjoint functors; 4. Generators and projectives; 5. Categories of fractions; 6. Flat functors and Cauchy completeness; 7. Bicategories and distributors; 8. Internal category theory; Bibliography; Index.

Vol. 2: Categories and Structures

Preface; Introduction; 1. Abelian categories; 2. Regular categories; 3. Algebraic theories; 4. Monads; 5. Accessible categories; 6. Enriched category theory; 7. Topological categories; 8. Fibred categories; Bibliography; Index.

Vol. 3: Categories of Sheaves

Preface; Introduction; 1. Locales; 2. Sheaves; 3. Grothendieck toposes; 4. The classifying topos; 5. Elementary toposes; 6. Internal logic of a topos; 7. The law of excluded middle; 8. The axiom of infinity; 9. Sheaves in a topos; Bibliography; Index.