Topos Theory

Incidentally, the reaction of one Cambridge colleague on learning that I’d appeared as a Dover reprint was ‘I didn’t know you were dead’. Peter Johnstone1

A short review of

  • P. T. Johnstone, Topos Theory , Academic Press 1977 (Paperback edition: Dover reprint 2014). xxiii + 367 pages.

Peter Johnstone’s classic text on topos theory from 1977 served as the standard reference in the field until the publication of MacLane-Moerdijk’s Sheaves in Geometry and Logic in 1992 and the monumental first two volumes of Sketches of an elephant in 2002, also by Johnstone. Topos Theory reportedly contains almost all results in topos theory known in the mid 1970s.

Although the author takes no prisoners the text is not really as unreadable as the introduction to the Elephant boasts but contains in a concise form what still constitutes the core of the subject.

It has also several unique features in comparison with its successor volumes in that it offers (somewhat more opiniated) remarks on the historical development of topos theory and an emphasis of the intuitionistic algebra and theory of spectrum prominent in the early 1970s, a chapter on cohomology theory and due to the recent paperback reprint an affordable price.

Table of contents

  • chap. 0. Preliminaries
  • chap. 1. Elementary Toposes
  • chap. 2. Internal Category Theory
  • chap. 3. Topologies and Sheaves
  • chap. 4. Geometric Morphisms
  • chap. 5. Logical Aspects of Topos Theory
  • chap. 6. Natural Number Objects
  • chap. 7. Theorems of Deligne and Barr
  • chap. 8. Cohomology
  • chap. 9. Topos Theory and Set Theory
  • Appendix Locally Internal Categories


  • Robert Seely, Review, P. T. Johnstone, Topos Theory , JSL 47 no.2 (1982) pp.448-450. (draft)
category: reference

Last revised on August 20, 2020 at 02:05:46. See the history of this page for a list of all contributions to it.