基于余代数和逗号范畴的M-粘着范畴
Towards M-Adhesive Categories based on Coalgebras and Comma Categories
摘要：
在这篇文章中，我们研究了幂集的几个扩展，包括任意嵌套的子集，并称之为超级集。这允许定义具有可能无限嵌套节点的图。另外，我们定义与边关联的边。由于我们使用了余代数结构，我们把这些图称为余递归图。研究了超幂集函子，并将其用于定义$\mathcal{M}$ -粘附范畴，这些范畴是$\mathcal{M}$ -粘附变换系统的基本范畴.因此，我们还证明了余代数$\mathbf{Sets}_F$是$\mathcal{M}$ -粘附范畴，只要函子$F:\mathbf{Sets}_F \to \mathbf{Sets}_F$沿着单态保持拉回。
英文摘要：
In this contribution we investigate several extensions of the powerset that comprise arbitrarily nested subsets, and call them superpower set. This allows the definition of graphs with possibly infinitely nested nodes. additionally we define edges that are incident to edges. Since we use coalgebraic constructions we refer to these graphs as corecursive graphs. The superpower set functors are examined and then used for the definition of $\mathcal{M}$-adhesive categories which are the basic categories for $\mathcal{M}$-adhesive transformation systems. So, we additionally show that coalgebras $\mathbf{Sets}_F$ are $\mathcal{M}$-adhesive categories provided the functor $F:\mathbf{Sets}_F \to \mathbf{Sets}_F$ preserves pullbacks along monomorphisms.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
