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A Pirashvili-type theorem for functors on non-empty finite sets

Abstract : Pirashvili's Dold-Kan type theorem for finite pointed sets follows from the identification in terms of surjections of the morphisms between the tensor powers of a functor playing the role of the augmentation ideal; these functors are projective. We give an unpointed analogue of this result: namely, we compute the morphisms between the tensor powers of the corresponding functor in the unpointed context. We also calculate the Ext groups between such objects, in particular showing that these functors are not projective; this is an important difference between the pointed and unpointed contexts. This work is motivated by our functorial analysis of the higher Hochschild homology of a wedge of circles.
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https://hal.archives-ouvertes.fr/hal-02945661
Contributor : Christine Vespa Connect in order to contact the contributor
Submitted on : Tuesday, September 22, 2020 - 2:51:24 PM
Last modification on : Tuesday, March 30, 2021 - 3:46:15 AM
Long-term archiving on: : Wednesday, December 23, 2020 - 6:13:23 PM

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  • HAL Id : hal-02945661, version 1
  • ARXIV : 2009.10966

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Geoffrey Powell, Christine Vespa. A Pirashvili-type theorem for functors on non-empty finite sets. 2020. ⟨hal-02945661⟩

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