2019
DOI: 10.1016/j.aim.2019.05.016
|View full text |Cite
|
Sign up to set email alerts
|

Monads and theories

Abstract: Given a locally presentable enriched category E together with a small dense full subcategory A of arities, we study the relationship between monads on E and identity-on-objects functors out of A, which we call Apretheories. We show that the natural constructions relating these two kinds of structure form an adjoint pair. The fixpoints of the adjunction are characterised as the A-nervous monads-those for which the conclusions of Weber's nerve theorem hold-and the A-theories, which we introduce here.The resultin… Show more

Help me understand this report
View preprint versions

Search citation statements

Order By: Relevance

Paper Sections

Select...
4
1

Citation Types

1
42
0

Year Published

2021
2021
2024
2024

Publication Types

Select...
6

Relationship

0
6

Authors

Journals

citations
Cited by 16 publications
(43 citation statements)
references
References 23 publications
1
42
0
Order By: Relevance
“…Definition 3.1. (Bourke and Garner (2019)). Let K be a category and A a small dense subcategory of K .…”
Section: Algebras In General Categoriesmentioning
confidence: 99%
See 4 more Smart Citations
“…Definition 3.1. (Bourke and Garner (2019)). Let K be a category and A a small dense subcategory of K .…”
Section: Algebras In General Categoriesmentioning
confidence: 99%
“…The resulting enriched Lawvere theories from Nishizawa and Power (2009) do not fit our aim to do universal algebra over a V -category K . Recently, Bourke and Garner (2019) introduced A -pretheories for every small dense subcategory A of K and related them to A -nervous enriched monads on K . Their pretheories perfectly suit our needs and describe λ-ary monads on every locally λ-presentable Vcategory K provided that V is locally λ-presentable as a closed category.…”
Section: Introductionmentioning
confidence: 99%
See 3 more Smart Citations