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In an article published in 2009, Dave Benson described, for a finite group G, the mod p homology of the space Ω(BG^∧_ p) — the loop space of the p-completion of BG — in purely algebraic terms. In joint work with Carles Broto and Ran Levi, we have tried to better understand Benson’s result by generalizing it. Among other things, we showed that when C is a small category, |C| is its geometric realization, R is a commutative ring, and |C|^+_R is a plus construction of |C| with respect to homology with coefficients in R, then H_∗(Ω(|C|^+_R); R) is the homology any chain complex of projective RC-modules that satisfies certain conditions. Benson’s theorem is then the special case where C is the category associated to a finite group G and R = F_p, so that p-completion appears as a special case of the plus construction.