Abstract
We give a new account of the correspondence, first established by Nishizawa-Power, between finitary monads and Lawvere theories over an arbitrary locally finitely presentable base. Our account explains this correspondence in terms of enriched category theory: the passage from a finitary monad to the corresponding Lawvere theory is exhibited as an instance of free completion of an enriched category under a class of absolute colimits. This extends work of the first author, who established the result in the special case of finitary monads and Lawvere theories over the category of sets; a novel aspect of the generalisation is its use of enrichment over a bicategory, rather than a monoidal category, in order to capture the monad-theory correspondence over all locally finitely presentable bases simultaneously.
Original language | English |
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Article number | 16 |
Pages (from-to) | 1-23 |
Number of pages | 23 |
Journal | Logical Methods in Computer Science |
Volume | 14 |
Issue number | 1 |
DOIs | |
Publication status | Published - 27 Feb 2018 |
Bibliographical note
Copyright the Author(s) 2018. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.Keywords
- Absolute colimits
- Enrichment in a bicategory
- Finitary monad
- Lawvere theory
- Locally finitely presentable category