Corpus ID: 2779544

# Enriched algebraic theories and monads for a system of arities

@article{LucyshynWright2015EnrichedAT,
title={Enriched algebraic theories and monads for a system of arities},
author={R. B. Lucyshyn-Wright},
journal={ArXiv},
year={2015},
volume={abs/1511.02920}
}
• R. B. Lucyshyn-Wright
• Published 2015
• Computer Science, Mathematics
• ArXiv
• Under a minimum of assumptions, we develop in generality the basic theory of universal algebra in a symmetric monoidal closed category $\mathcal{V}$ with respect to a specified system of arities $j:\mathcal{J} \hookrightarrow \mathcal{V}$. Lawvere's notion of algebraic theory generalizes to this context, resulting in the notion of single-sorted $\mathcal{V}$-enriched $\mathcal{J}$-cotensor theory, or $\mathcal{J}$-theory for short. For suitable choices of $\mathcal{V}$ and $\mathcal{J}$, such… CONTINUE READING
12 Citations

#### Paper Mentions

Commutants for Enriched Algebraic Theories and Monads
• 3
• PDF
Algebraic Theories and Commutativity in a Sheaf Topos
• Boaz Haberman
• Mathematics, Computer Science
• Appl. Categorical Struct.
• 2020
Convex Spaces, Affine Spaces, and Commutants for Algebraic Theories
• 2
• PDF
Enriched Lawvere Theories for Operational Semantics
• Mathematics, Computer Science
• ACT
• 2019

#### References

SHOWING 1-10 OF 58 REFERENCES
Notions of Lawvere Theory
• Mathematics, Computer Science
• Appl. Categorical Struct.
• 2011
• 32
• PDF
Elements of a theory of algebraic theories
• M. Hyland
• Mathematics, Computer Science
• Theor. Comput. Sci.
• 2014
• 10
• PDF