A Variety Theorem for Relational Universal Algebra

  title={A Variety Theorem for Relational Universal Algebra},
  author={Chad Nester},
We develop an analogue of universal algebra in which generating symbols are interpreted as relations. We prove a variety theorem for these relational algebraic theories, in which we find that their categories of models are precisely the ’definable categories’. The syntax of our relational algebraic theories is string-diagrammatic, and can be seen as an extension of the usual term syntax for algebraic theories. 



Functorial Semantics for Relational Theories

The concept of Frobenius theory is introduced as a generalisation of Lawvere's functorial semantics approach to categorical universal algebra and takes their models in the category of sets and relations.

Functorial semantics for partial theories

A Lawvere-style definition for partial theories, extending the classical notion of equational theory by allowing partially defined operations, and demonstrating the expressivity of such equational theories by considering a number of examples.

On the duality between varieties and algebraic theories

Abstract. Every variety $ \mathcal{V} $ of finitary algebras is known to have an essentially unique algebraic theory $ Th (\mathcal{V}) $ which is Cauchy complete, i.e., all idempotents split in $ Th

Algebraic Theories: A Categorical Introduction to General Algebra

Algebraic theories, introduced as a concept in the 1960s, have been a fundamental step towards a categorical view of general algebra. Moreover, they have proved very useful in various areas of

On the Structure of Generalized Effect Algebras and Separation Algebras

This work presents an orderly algorithm for constructing all nonisomorphic generalized pseudoeffect algebras with n elements and uses it to compute these algeBRas with up to 10 elements.

On the Structure of Abstract Algebras

  • G. BirkhoffP. Hall
  • Mathematics
    Mathematical Proceedings of the Cambridge Philosophical Society
  • 1935
The following paper is a study of abstract algebras qua abstract algebras. As no vocabulary suitable for this purpose is current, I have been forced to use a number of new terms, and extend the

The geometry of tensor calculus, I

Isotropy of Algebraic Theories

Exact Categories

On Regular Rings.

  • J. von Neumann
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1936
This chapter presents the basic properties of general regular rings, the nature and use of idempotents, the class of all principal right ideals (left ideals) as a complemented modular lattice, and other general properties of regular rings which are useful in the remaining chapters.