⋆-Autonomous categories: once more around the track
Michael Barr · Theory and applications of categories · 1999
. This represents a new and more comprehensive approach to the - autonomous categories constructed in the monograph [Barr, 1979]. The main tool in the new approach is the Chu construction. The main conclusion is that the category of separated extensional Chu objects for certain kinds of equational categories is equivalent to two usually distinct subcategories of the categories of uniform algebras of those categories. 1. Introduction The monograph [Barr, 1979] was devoted to the investigation of -autonomous categories. Most of the book was devoted to the discovery of -autonomous categories as full subcategories of seven different categories of uniform or topological algebras over concrete categories that were either equational or reflective subcategories of equational categories. The base categories were: 1. vector spaces over a discrete field; 2. vector spaces over the real or complex numbers; 3. modules over a ring with a dualizing module; 4. abelian groups; 5. modules ove...