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
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