Absolute Colimits

Ross Street; Richard Garner

doi:10.1007/s10485-026-09847-1

Absolute Colimits

Ross Street, Richard Garner

School of Mathematical and Physical Sciences

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Abstract

In the context of enriched category theory, we give necessary and sufficient conditions for a module morphism α:M→C(F,Z) to exhibit a functor Z:A→C as an absolute M-weighted colimit of a functor F:B→C. 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′.

Original language	English
Article number	43
Pages (from-to)	1-13
Number of pages	13
Journal	Applied Categorical Structures
Volume	34
Issue number	5
DOIs	https://doi.org/10.1007/s10485-026-09847-1
Publication status	Published - Oct 2026

Bibliographical note

Keywords

Enriched Category
Module
Weighted Colimit

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10.1007/s10485-026-09847-1Licence: CC BY

Publisher version (open access)Final published version, 285 KBLicence: CC BY

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title = "Absolute Colimits",

abstract = "In the context of enriched category theory, we give necessary and sufficient conditions for a module morphism α:M→C(F,Z) to exhibit a functor Z:A→C as an absolute M-weighted colimit of a functor F:B→C. 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′.",

keywords = "Enriched Category, Module, Weighted Colimit",

author = "Ross Street and Richard Garner",

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AU - Street, Ross

AU - Garner, Richard

N1 - © The Author(s) 2026. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

PY - 2026/10

Y1 - 2026/10

N2 - In the context of enriched category theory, we give necessary and sufficient conditions for a module morphism α:M→C(F,Z) to exhibit a functor Z:A→C as an absolute M-weighted colimit of a functor F:B→C. 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′.

AB - In the context of enriched category theory, we give necessary and sufficient conditions for a module morphism α:M→C(F,Z) to exhibit a functor Z:A→C as an absolute M-weighted colimit of a functor F:B→C. 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′.

KW - Enriched Category

KW - Module

KW - Weighted Colimit

UR - https://www.scopus.com/pages/publications/105045124939

UR - https://purl.org/au-research/grants/arc/DP190102432

UR - https://purl.org/au-research/grants/arc/DP160101519

U2 - 10.1007/s10485-026-09847-1

DO - 10.1007/s10485-026-09847-1

M3 - Article

AN - SCOPUS:105045124939

SN - 0927-2852

VL - 34

SP - 1

EP - 13

JO - Applied Categorical Structures

JF - Applied Categorical Structures

IS - 5

M1 - 43

ER -

Absolute Colimits

Abstract

Bibliographical note

Keywords

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Absolute Colimits

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Projects

Working synthetically in higher categorical structures

Monoidal categories and beyond: new contexts and new applications

Cite this