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<p>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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月16日

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  • Amartya Goswami,
  • Zurab Janelidze,
  • Graham Manuell

摘要

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.