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 Johnstone^{1}

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

References

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