Parametrized equivalence relation on the global class of morphisms of a category and frame-theoretic examples
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908831484739584 |
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| author | Idrissi, Nizar El |
| author_facet | Idrissi, Nizar El |
| contents | We introduce an equivalence relation on the global class of morphisms of a category that extends several classical notions of equivalence in mathematics. We show that the standard group-action equivalence is a special case of our framework. A more interesting example is provided by an equivalence relation defined on the class of Bessel families and based on a coarse invariant that is the pointwise norm of the analysis operator of the Bessel family -- this is also a special case of our framework, and the formalism developed here can be seen as a first step toward a categorical invariant theory for Bessel families and continuous frames. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_12363 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Parametrized equivalence relation on the global class of morphisms of a category and frame-theoretic examples Idrissi, Nizar El Category Theory Functional Analysis 18A99, 18B10, 18B40, 46M15, 42C15 We introduce an equivalence relation on the global class of morphisms of a category that extends several classical notions of equivalence in mathematics. We show that the standard group-action equivalence is a special case of our framework. A more interesting example is provided by an equivalence relation defined on the class of Bessel families and based on a coarse invariant that is the pointwise norm of the analysis operator of the Bessel family -- this is also a special case of our framework, and the formalism developed here can be seen as a first step toward a categorical invariant theory for Bessel families and continuous frames. |
| title | Parametrized equivalence relation on the global class of morphisms of a category and frame-theoretic examples |
| topic | Category Theory Functional Analysis 18A99, 18B10, 18B40, 46M15, 42C15 |
| url | https://arxiv.org/abs/2602.12363 |