Geodesic
A Pirashvili-type theorem for functors on non-empty finite sets
Glasgow mathematical journal, Tome 65 (2023) no. 1, pp. 1-61

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DOI

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.
DOI : 10.1017/S0017089522000039
Mots-clés : category of finite sets and surjections, comonad on Gamma-modules, Koszul complex, FIop cohomology 
Powell, Geoffrey; Vespa, Christine. A Pirashvili-type theorem for functors on non-empty finite sets. Glasgow mathematical journal, Tome 65 (2023) no. 1, pp. 1-61. doi: 10.1017/S0017089522000039
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     year = {2023},
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