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Absolute colimits

Year: 2026
Type: preprint
Abstract: 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 $M'$.
DOI: 10.48550/arxiv.2608.25607
Open Access status: green
OpenAlex ID: W7204485639
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