### Abstract

Original language | English |
---|---|

Pages (from-to) | 1--23 |

Number of pages | 14 |

Journal | Logical Methods in Computer Science |

State | Accepted/In press - 1 Jan 2018 |

### Keywords

- bicategory, enriched category, monad, Lawvere theory

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Logical Methods in Computer Science*, 1--23.

**An enriched view on the extended finitary monad-Lawvere theory correspondence.** / Power, Anthony; Garner, Richard.

Research output: Contribution to journal › Article

*Logical Methods in Computer Science*, pp. 1--23.

}

TY - JOUR

T1 - An enriched view on the extended finitary monad-Lawvere theory correspondence

AU - Power,Anthony

AU - Garner,Richard

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

KW - bicategory, enriched category, monad, Lawvere theory

M3 - Article

SP - 1

EP - 23

JO - Logical Methods in Computer Science

T2 - Logical Methods in Computer Science

JF - Logical Methods in Computer Science

SN - 1860-5974

ER -