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<p>This paper concerns exponential contravariant functors on free groups. We obtain an equivalence of categories between analytic, exponential contravariant functors on free groups and conilpotent cocommutative Hopf algebras. This result explains how equivalences of categories obtained previously by Pirashvili and by Powell interact. Moreover, we obtain an equivalence between the categories of outer, exponential contravariant functors on free groups and bicommutative Hopf algebras. We also go further by introducing a subclass of analytic, contravariant functors on free groups, called <i>primitive</i> functors; and prove an equivalence between primitive, exponential contravariant functors and primitive cocommutative Hopf algebras.</p>

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On analytic exponential functors on free groups

  • 期刊论文

  • 发表日期：

    2025年12月3日

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  • Minkyu Kim,
  • Christine Vespa

摘要

This paper concerns exponential contravariant functors on free groups. We obtain an equivalence of categories between analytic, exponential contravariant functors on free groups and conilpotent cocommutative Hopf algebras. This result explains how equivalences of categories obtained previously by Pirashvili and by Powell interact. Moreover, we obtain an equivalence between the categories of outer, exponential contravariant functors on free groups and bicommutative Hopf algebras. We also go further by introducing a subclass of analytic, contravariant functors on free groups, called primitive functors; and prove an equivalence between primitive, exponential contravariant functors and primitive cocommutative Hopf algebras.