Frobenius reciprocity, modular connections, lattice isomorphism theorem and abstract principal ideals

Fuente: arXiv
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Hauptverfasser: Goswami, Amartya, Janelidze, Zurab, Manuell, Graham
Format: Preprint
Veröffentlicht: 2025
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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