Absolute colimits

Richard Garner; Ross Street

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arXiv · 2608.25607

Absolute colimits

Richard Garner·Ross Street

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Abstract

In the context of enriched category theory, we give necessary and sufficient conditions for a module morphism $\alpha \dd M \to \CC(F,Z)$ 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 $M'$.

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Richard Garner, Ross Street. 2026-08-26. Absolute colimits. https://arxiv.org/abs/2608.25607

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