# A Variety Theorem for Relational Universal Algebra

@article{Nester2021AVT, title={A Variety Theorem for Relational Universal Algebra}, author={Chad Nester}, journal={ArXiv}, year={2021}, volume={abs/2105.04958} }

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.

## References

SHOWING 1-10 OF 35 REFERENCES

### Functorial Semantics for Relational Theories

- MathematicsArXiv
- 2017

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

- MathematicsProc. ACM Program. Lang.
- 2021

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

- Mathematics
- 2003

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

- Mathematics
- 2010

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

- MathematicsRAMiCS
- 2018

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

- MathematicsMathematical 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…

### On Regular Rings.

- MathematicsProceedings 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.