A criterion for a Hurewicz cofibration to be a Quillen cofibration
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917259531780096 |
|---|---|
| author | Ronan, Andrew |
| author_facet | Ronan, Andrew |
| contents | In this paper, we prove that $h$-cofibrations between $q$-cofibrant spaces are $q$-cofibrations. We also present a number of applications, including a pushout-product property for symmetrizable cofibrations, a local-to-global gluing lemma for $q$-cofibrations, a proof that $q$-fibrations between $q$-cofibrant spaces are $h$-fibrations, and an alternative proof of Waner's theorem on $G$-spaces with the $G$-homotopy type of a $G$-CW complex in fibre sequences. Moreover, all of the above generalises readily to the equivariant context, and so we work in the more general equivariant setting throughout. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_08317 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A criterion for a Hurewicz cofibration to be a Quillen cofibration Ronan, Andrew Algebraic Topology In this paper, we prove that $h$-cofibrations between $q$-cofibrant spaces are $q$-cofibrations. We also present a number of applications, including a pushout-product property for symmetrizable cofibrations, a local-to-global gluing lemma for $q$-cofibrations, a proof that $q$-fibrations between $q$-cofibrant spaces are $h$-fibrations, and an alternative proof of Waner's theorem on $G$-spaces with the $G$-homotopy type of a $G$-CW complex in fibre sequences. Moreover, all of the above generalises readily to the equivariant context, and so we work in the more general equivariant setting throughout. |
| title | A criterion for a Hurewicz cofibration to be a Quillen cofibration |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2602.08317 |