The aim of this paper is to obtain an effective rule (or algorithm) for distinguishing sentences from nonsentences, which works not only for the formal languages of interest to the mathematical… Expand

Preface Part I. Introduction to Category Theory: Part II. Cartesian Closed Categories and Calculus: Part III. Type Theory and Toposes: Part IV. Representing Numerical Functions in Various Categories… Expand

A protogroup is an ordered monoid in which each element a has both a left proto-inverse al such that ala ≤ 1 and a right protoinverse ar such that aar ≤ 1.Expand

This book is an introduction to the theory of associative rings and their modules, designed primarily for graduate students. The standard topics on the structure of rings are covered, with a… Expand

Abstract A diagram chasing technique generalizing the ‘two-square’ lemma of homological algebra is extended from Mal'cev varieties to Mal'cev categories: regular categories in which all reflexive… Expand