AI 中文总结
该研究在富集范畴论中，给出了模态射使函子成为绝对M-加权余极限的充要条件，综述了绝对权的判据，并证明绝对M-加权余极限可视为绝对权M'的加权余极限。
AI 中文摘要
在富集范畴论的语境下，我们给出了模态射α: M→CC(F,Z)使函子Z: CA→CC成为函子F: CB→CC的绝对M-加权余极限的充要条件。我们还通过简短证明，综述了权M本身为绝对权的各类判据，即任何M-加权余极限都是绝对的。最后，我们证明了任何绝对M-加权余极限都可视为绝对权M'的加权余极限。
英文摘要
In the context of enriched category theory, we give necessary and sufficient conditions for a module morphism $α\dd M \to \CC(F,Z)$ to exhibit a functor $Z\dd \CA\to \CC$ as an absolute $M$-weighted colimit of a functor ${F\dd \CB\to \CC}$. We also review, with short proofs, the various criteria for the weight $M$ itself to be absolute, in the sense that any $M$-weighted colimit is absolute. Finally, we prove that any absolute $M$-weighted colimit can be viewed as a colimit weighted by an absolute weight $M'$.
CommentsReferences [1], [9], [14], [15] are added thanks to comments from Nathanael Arkor, and some words: see last sentence of second last paragraph of the Introduction and just before Theorem 2.1
Journal refAbsolute colimits, Applied Categorical Structures 34:43 (dedicated to Bob Paré, 2026)
