nLab Handbook of Categorical Algebra



Category Theory

Topos Theory

topos theory



Internal Logic

Topos morphisms

Extra stuff, structure, properties

Cohomology and homotopy

In higher category theory


This entry is to record the monograph

on category theory, categorical algebra and topos theory.

Book review:


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.

category: reference

Last revised on August 3, 2021 at 08:19:57. See the history of this page for a list of all contributions to it.