# Diagrammatic presentations of enriched monads and varieties for a subcategory of arities

@inproceedings{LucyshynWright2022DiagrammaticPO, title={Diagrammatic presentations of enriched monads and varieties for a subcategory of arities}, author={Rory B. B. Lucyshyn-Wright and Jason Parker}, year={2022} }

The theory of presentations of enriched monads was developed by Kelly, Power, and Lack, following classic work of Lawvere, and has been generalized to apply to subcategories of arities in recent work of Bourke-Garner and the authors. We argue that, while theoretically elegant and structurally fundamental, such presentations of enriched monads can be inconvenient to construct directly in practice, as they do not directly match the deﬁnitional procedures used in constructing many categories of…

## One Citation

### Locally bounded enriched categories

- Mathematics
- 2021

We deﬁne and study the notion of a locally bounded enriched category over a (locally bounded) symmetric monoidal closed category, generalizing the locally bounded ordinary categories of Freyd and…

## References

SHOWING 1-10 OF 53 REFERENCES

### Presentations and algebraic colimits of enriched monads for a subcategory of arities

- Mathematics
- 2022

We develop a general framework for studying signatures, presentations, and algebraic colimits of enriched monads for a subcategory of arities, even when the base of enrichment V is not locally…

### Adjunctions whose counits are coequalizers, and presentations of finitary enriched monads

- Mathematics
- 1993

### BASIC CONCEPTS OF ENRICHED CATEGORY THEORY

- MathematicsElements of ∞-Category Theory
- 2005

Although numerous contributions from divers authors, over the past fifteen years or so, have brought enriched category theory to a developed state, there is still no connected account of the theory,…

### Monads need not be endofunctors

- MathematicsLog. Methods Comput. Sci.
- 2010

A generalization of monads is introduced, called relative monads, allowing for underlying functors between different categories, and it is shown that the Kleisli and Eilenberg-Moore constructions carry over to relative monad and are related to relative adjunctions.

### Finite-product-preserving functors, Kan extensions, and strongly-finitary 2-monads

- MathematicsAppl. Categorical Struct.
- 1993

It is shown that endofunctors of this kind are closed under composition involves a lemma on left Kan extensions along a coproduct-preserving functor in the context of cartesian closed categories, closely related to an earlier result of Borceux and Day.