Ephemeral Modules and Scott Sheaves on a Continuous Poset
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909403738800128 |
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| author | Harsu, Manu Hyry, Eero |
| author_facet | Harsu, Manu Hyry, Eero |
| contents | By utilizing domain theory, we generalize the notion of an ephemeral module to the so-called continuous posets. We investigate the quotient category of persistence modules by the Serre subcategory of ephemeral modules and show that it is equivalent to the category of sheaves on the Scott topology. Furthermore, we study the metric properties of persistence modules via this equivalence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_16235 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ephemeral Modules and Scott Sheaves on a Continuous Poset Harsu, Manu Hyry, Eero Algebraic Topology Commutative Algebra Representation Theory 55N31, 16G20, 13D07 By utilizing domain theory, we generalize the notion of an ephemeral module to the so-called continuous posets. We investigate the quotient category of persistence modules by the Serre subcategory of ephemeral modules and show that it is equivalent to the category of sheaves on the Scott topology. Furthermore, we study the metric properties of persistence modules via this equivalence. |
| title | Ephemeral Modules and Scott Sheaves on a Continuous Poset |
| topic | Algebraic Topology Commutative Algebra Representation Theory 55N31, 16G20, 13D07 |
| url | https://arxiv.org/abs/2411.16235 |