Let F --> E --> B be a fibration with B a simply connected finite type CW complex. In this paper we consider the relations between the category of E and the growth and the grade of the homology of F as a module over the loop space homology of B.
Decoster, C., & Félix, Y. (1996). Category, growth and grade in a fibration. Journal of Pure and Applied Algebra, 113(2), 145-157. https://doi.org/10.1016/0022-4049(96)00017-5 (Original work published 1996)