On a fibrational construction for optics, lenses, and Dialectica categories
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910748312076288 |
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| author | Capucci, Matteo Gavranović, Bruno Malik, Abdullah Rios, Francisco Weinberger, Jonathan |
| author_facet | Capucci, Matteo Gavranović, Bruno Malik, Abdullah Rios, Francisco Weinberger, Jonathan |
| contents | Categories of lenses/optics and Dialectica categories are both comprised of bidirectional morphisms of basically the same form. In this work we show how they can be considered a special case of an overarching fibrational construction, generalizing Hofstra's construction of Dialectica fibrations and Spivak's construction of generalized lenses. This construction turns a tower of Grothendieck fibrations into another tower of fibrations by iteratively twisting each of the components, using the opposite fibration construction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_16388 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a fibrational construction for optics, lenses, and Dialectica categories Capucci, Matteo Gavranović, Bruno Malik, Abdullah Rios, Francisco Weinberger, Jonathan Category Theory Information Theory Logic in Computer Science 18M35, 18D30, 18M05, 03G30, 03B38 F.4.1 Categories of lenses/optics and Dialectica categories are both comprised of bidirectional morphisms of basically the same form. In this work we show how they can be considered a special case of an overarching fibrational construction, generalizing Hofstra's construction of Dialectica fibrations and Spivak's construction of generalized lenses. This construction turns a tower of Grothendieck fibrations into another tower of fibrations by iteratively twisting each of the components, using the opposite fibration construction. |
| title | On a fibrational construction for optics, lenses, and Dialectica categories |
| topic | Category Theory Information Theory Logic in Computer Science 18M35, 18D30, 18M05, 03G30, 03B38 F.4.1 |
| url | https://arxiv.org/abs/2403.16388 |