Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2304.11348 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916178448875520 |
|---|---|
| author | Schiavo, Lorenzo Dello |
| author_facet | Schiavo, Lorenzo Dello |
| contents | A measurable map between measure spaces is shown to have bounded compression if and only if its image via the measure-algebra functor is Lipschitz-continuous w.r.t. the measure-algebra distances. This provides a natural interpretation of maps of bounded compression/deformation by means of the measure-algebra functor and corroborates the assertion that maps of bounded deformation are the natural class of morphisms for the category of complete and separable metric measure spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_11348 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Characterization of Maps of Bounded Compression Schiavo, Lorenzo Dello Metric Geometry Category Theory 28A60 A measurable map between measure spaces is shown to have bounded compression if and only if its image via the measure-algebra functor is Lipschitz-continuous w.r.t. the measure-algebra distances. This provides a natural interpretation of maps of bounded compression/deformation by means of the measure-algebra functor and corroborates the assertion that maps of bounded deformation are the natural class of morphisms for the category of complete and separable metric measure spaces. |
| title | A Characterization of Maps of Bounded Compression |
| topic | Metric Geometry Category Theory 28A60 |
| url | https://arxiv.org/abs/2304.11348 |