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Let R be a commutative Noetherian ring, I,J ideals of R and M a finitely generated R-module. Let F be a covariant R-linear functor from the category of finitely generated R-modules to itself. We first show that if F is coherent, then the sets AssRF(M/InM), AssRF(In−1M/InM) and the values depthJF(M/InM), depthJF(In−1M/InM) become independent of n for large n. Next, we consider several examples in which...