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arXiv · 2502.06010

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

Amartya Goswami·Zurab Janelidze·Graham Manuell
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Abstract

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.

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Amartya Goswami, Zurab Janelidze, Graham Manuell. 2025-02-09. Frobenius reciprocity, modular connections, lattice isomorphism theorem and abstract principal ideals. https://arxiv.org/abs/2502.06010

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