  We provide a sufficient condition that ensures the nilpotency of
endomorphisms universally of trace zero of Schur-finite objects in a category
of homological type, i.e., a Q-linear tensor category with a tensor functor to
super vector spaces. This generalizes previous results about finite-dimensional
objects, in particular by Kimura in the category of motives. We also present
some facts which suggest that this might be the best generalization possible of
this line of proof. To get the result we prove an identity of trace relations
on super vector spaces which has an independent interest in the field of
combinatorics. Our main tool is Berele-Regev's theory of Hook Schur functions.
We use their generalization of the classic Schur-Weyl duality to the "super"
case, together with their factorization formula.
