一句话：推广范畴的生成元-关系表示，证明在对象模等价时商、局部化与正规形三种构造在相干条件下一致，并扩展至幺半范畴。
范畴的表示通常由对象与态射生成元及态射关系给出。本文允许对象本身模去由等式生成元描述的等价关系：当这些生成元构成收敛的抽象重写系统时，可自然定义三种范畴：把等式生成元变为恒等等价的商范畴、形式添加逆的局部化范畴，以及限制到正规对象的范畴。作者给出表示上的相干条件，证明三者一致，从而推广群表示的经典结果，并将条件扩展到幺半范畴的表示。
Presentations of categories are a well-known algebraic tool to provide descriptions of categories by means of generators, for objects and morphisms, and relations on morphisms. We generalize here this notion, in order to consider situations where the objects are considered modulo an equivalence relation, which is described by equational generators. When those form a convergent (abstract) rewriting system on objects, there are three very natural constructions that can be used to define the category which is described by the presentation: one consists in turning equational generators into identities (i.e. considering a quotient category), one consists in formally adding inverses to equational generators (i.e. localizing the category), and one consists in restricting to objects which are normal forms. We show that, under suitable coherence conditions on the presentation, the three constructions coincide, thus generalizing celebrated results on presentations of groups, and we extend those conditions to presentations of monoidal categories.
DOI 原文 · arXiv · PDF（开放获取） · DBLP
@article{CurienM17,
title = {Coherent Presentations of Monoidal Categories},
author = {Pierre-Louis Curien and Samuel Mimram},
journal = {Logical Methods in Computer Science},
volume = {Volume 13, Issue 3},
year = {2017},
doi = {10.23638/lmcs-13(3:31)2017}
}