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 morphisms between tensor powers a functor playing role augmentation ideal; these functors are projective. We give an unpointed analogue this result: namely, we compute corresponding context. also calculate Ext groups such objects, particular showing that not projective; is important difference and contexts. This work motivated by our functorial analysis higher Hochschild homology wedge circles.