Lawvere’s Frobenius Reciprocity, the Modular Connections of Grandis and Dilworth’s Abstract Principal Ideals

Amartya Goswami; Zurab Janelidze; Graham Manuell

doi:10.1007/s10485-025-09808-0

Lawvere’s Frobenius Reciprocity, the Modular Connections of Grandis and Dilworth’s Abstract Principal Ideals

Amartya Goswami, Zurab Janelidze, Graham Manuell

Mathematics and Applied Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	16
Journal	Applied Categorical Structures
Volume	33
Issue number	3
DOIs	https://doi.org/10.1007/s10485-025-09808-0
Publication status	Published - Jun 2025

Keywords

Abstract ideal theory
Adjunction
Connection
Frobenius reciprocity
Grandis exact category
Lattice
Lattice isomorphism theorem
Modular connection
Modular lattice
Noetherian form
Principal element
Principal mapping
Protomodular category
Quantale
Range-closed mapping
Residuated map

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science
Algebra and Number Theory

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10.1007/s10485-025-09808-0

Cite this

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Lawvere’s Frobenius Reciprocity, the Modular Connections of Grandis and Dilworth’s Abstract Principal Ideals

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Keywords

ASJC Scopus subject areas

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