一句话：把粘合范畴的刻画与 Grothendieck topos 嵌入定理推广到 M,N-粘合范畴，并引入 N-粘合态射。
粘合与拟粘合范畴为代数图重写系统提供统一框架。本文研究近期提出的 M,N-粘合范畴，旨在推广（拟）粘合性。作者引入 N-粘合态射，将 M,N-粘合性刻画为子对象偏序集上的条件；并证明任一 M,N-粘合范畴都可经保持拉回与 M,N-推出的函子嵌入到 Grothendieck topos 中。该结果统一并扩展了已知的（拟）粘合范畴嵌入定理，为代数图重写中更精细的推出结构提供范畴论基础。
Adhesive and quasiadhesive categories provide a general framework for the study of algebraic graph rewriting systems. In a quasiadhesive category any two regular subobjects have a join which is again a regular subobject. Vice versa, if regular monos are adhesive, then the existence of a regular join for any pair of regular subobjects entails quasiadhesivity. It is also known (quasi)adhesive categories can be embedded in a Grothendieck topos via a functor preserving pullbacks and pushouts along (regular) monomorphisms. In this paper we extend these results to $\mathcal{M}, \mathcal{N}$-adhesive categories, a concept recently introduced to generalize the notion of (quasi)adhesivity. We introduce the notion of $\mathcal{N}$-adhesive morphism, which allows us to express $\mathcal{M}, \mathcal{N}$-adhesivity as a condition on the subobjects' posets. Moreover, $\mathcal{N}$-adhesive morphisms allows us to show how an $\mathcal{M},\mathcal{N}$-adhesive category can be embedded into a Grothendieck topos, preserving pullbacks and $\mathcal{M}, \mathcal{N}$-pushouts.
DOI 原文 · arXiv · PDF（开放获取） · DBLP
@article{CastelnovoM25,
title = {On The Axioms Of $\mathcal{M},\mathcal{N}$-Adhesive Categories},
author = {Davide Castelnovo and Marino Miculan},
journal = {Logical Methods in Computer Science},
volume = {Volume 21, Issue 1},
year = {2025},
doi = {10.46298/lmcs-21(1:22)2025}
}