Categories, allegories. (English) Zbl 0698.18002

Freyd, Peter J.; Scedrov, André

North-Holland Mathematical Library, 39. Amsterdam etc.: North-Holland. xvii, 296 p. Dfl. 140.00/hbk; Dfl. 50.00/pbk (1990).

This book consists of two parts. The first part is devoted to the fundamentals of geometric logic, in which the four major concepts of modern mathematics merge; natural transformations introduced by Eilenberg and MacLane in the 1940’s, adjoint functors invented by Kan in the late 1950’s, sheaves formulated by Lazard in the late 1940’s, and topoi studied by Grothendieck’s school in the 1950’s and early 1960’s. The second part deals with general calculi of relations called allegories. The book should be of interest to category theorists, mathematical logicians and theoretical computer scientists.

Reviewer: H.Nishimura

MSC:

18B25	Topoi
18-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to category theory
18-02	Research exposition (monographs, survey articles) pertaining to category theory

Keywords:

geometric logic; natural transformations; adjoint functors; sheaves; topoi; allegories