Categories, Allegories

Categories, Allegories is a highly original work on categorical algebra by Peter Freyd and Andre Scedrov.

  • Peter Freyd and Andre Scedrov, Categories, Allegories, Mathematical Library Vol 39, North-Holland (1990). ISBN 978-0-444-70368-2.

(sometimes whimsically referred to as “Cats, Alligators” or “Cats and Alligators”).

On the Categories side, the book centers on that part of categorical algebra that studies exactness properties, or other properties enjoyed by nice or convenient categories such as toposes, and their relationship to logic (for example, geometric logic). A major theme throughout is the possibility of representation theorems (aka completeness theorems or embedding theorems) for various categorical structures, spanning back now about five decades (as of this writing) to the original embedding theorems for abelian categories, such as the Freyd-Mitchell embedding theorem.

On the Allegories side: it may be said they were first widely publicized in this book. They comprise many aspects of relational algebra corresponding to the categorical algebra studied in the first part of the book.

The book, while it covers an extraordinary amount of ground in less than 300 pages, is fairly idiosyncratic, especially in the choice of terminology and in the overall arrangement (designed to be self-contained for the diligent reader). There is no list of references given.

category: reference

Revised on August 25, 2012 22:45:28 by Urs Schreiber (