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<p>We introduce regular sequences and associated Koszul resolutions for monoids in the category of functors over an essentially small linear symmetric monoidal category. Next we define polynomials over such monoids. We compute the Hochschild cohomology functors and prove a relative analog of Hilbert’s syzygy theorem for polynomials over <i>tensor idempotent commutative monoids</i>.</p>

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Koszul complex for linear monoidal functors

  • 期刊论文

  • 发表日期：

    2026年5月13日

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  • Serge Bouc,
  • Nadia Romero

摘要

We introduce regular sequences and associated Koszul resolutions for monoids in the category of functors over an essentially small linear symmetric monoidal category. Next we define polynomials over such monoids. We compute the Hochschild cohomology functors and prove a relative analog of Hilbert’s syzygy theorem for polynomials over tensor idempotent commutative monoids.