Frobenius reciprocity, modular connections, lattice isomorphism theorem and abstract principal ideals
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911177226846208 |
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| author | Goswami, Amartya Janelidze, Zurab Manuell, Graham |
| author_facet | Goswami, Amartya Janelidze, Zurab Manuell, Graham |
| contents | The purpose of this short note is to fill a gap in the literature: Frobenius reciprocity in the theory of doctrines is closely related to modular connections in projective homological algebra and the notion of a principal element in abstract commutative ideal theory. These concepts are based on particular properties of Galois connections which play an important role also in the abstract study of group-like structures from the perspective of categorical/universal algebra; such role stems from a classical and basic result in group theory: the lattice isomorphism theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_06010 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Frobenius reciprocity, modular connections, lattice isomorphism theorem and abstract principal ideals Goswami, Amartya Janelidze, Zurab Manuell, Graham Rings and Algebras Category Theory 06A06, 13A15, 03G30, 20J99, 18G50, 06C05, 18E13, 08B05 The purpose of this short note is to fill a gap in the literature: Frobenius reciprocity in the theory of doctrines is closely related to modular connections in projective homological algebra and the notion of a principal element in abstract commutative ideal theory. These concepts are based on particular properties of Galois connections which play an important role also in the abstract study of group-like structures from the perspective of categorical/universal algebra; such role stems from a classical and basic result in group theory: the lattice isomorphism theorem. |
| title | Frobenius reciprocity, modular connections, lattice isomorphism theorem and abstract principal ideals |
| topic | Rings and Algebras Category Theory 06A06, 13A15, 03G30, 20J99, 18G50, 06C05, 18E13, 08B05 |
| url | https://arxiv.org/abs/2502.06010 |