一句话：用富集范畴论重新解释任意局部有限可表示基上的有限单子与 Lawvere 理论对应，并将其归约为绝对余极限下的自由完备化。
本文重新审视 Nishizawa 与 Power 建立的对应关系：在任意局部有限可表示（locally finitely presentable）基范畴上，有限单子（finitary monad）与 Lawvere 理论之间存在对应。作者用富集范畴论给出新解释，将从有限单子到相应 Lawvere 理论的构造刻画为在一类绝对余极限（absolute colimits）下对富集范畴的自由完备化。该工作推广了第一作者在集合范畴这一特殊情形下的结果；其新颖之处在于使用双范畴（bicategory）而非幺半范畴作为富集基，从而能够同时捕捉所有局部有限可表示基上的单子–理论对应。
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.Comment: 24 pages
@article{paperbot424,
title = {An enriched view on the extended finitary monad--Lawvere theory correspondence},
author = {Richard Garner and John Power},
journal = {Logical Methods in Computer Science},
volume = {Volume 14, Issue 1},
year = {2018},
doi = {10.23638/lmcs-14(1:16)2018}
}