一句话：在带因子分解系统的范畴中统一刻画余代系统的极小性与最小化，并给出可达性与可观测性最小化及可顺序化条件。
论文研究基于状态的系统最小化，即在不改变语义的前提下减少状态数，并将其分解为删除不必要状态与合并冗余状态两个方面。作者在余代数框架下，于配备因子分解系统的一般范畴中定义抽象的极小性与最小化概念，给出保证最小化唯一性、存在性与函子性的范畴条件。这些结果的证明可实例化为标准余代文献中的可达性最小化与可观测性最小化。最后，文章分析两个最小化方面的交互，并给出它们能以任意顺序复合（如自动机最小化）的判别条件。该更新版修正了图 10 中的错误。
For the minimization of state-based systems (i.e. the reduction of the number of states while retaining the system's semantics), there are two obvious aspects: removing unnecessary states of the system and merging redundant states in the system. In the present article, we relate the two minimization aspects on coalgebras by defining an abstract notion of minimality. The abstract notions minimality and minimization live in a general category with a factorization system. We will find criteria on the category that ensure uniqueness, existence, and functoriality of the minimization aspects. The proofs of these results instantiate to those for reachability and observability minimization in the standard coalgebra literature. Finally, we will see how the two aspects of minimization interact and under which criteria they can be sequenced in any order, like in automata minimization. This is an updated version that fixes a mistake in Figure 10