@DiracDeltaFunk Modulo set theoretic issues, use AoC to get a discontinuous automorphism f of ℝ, choose a basis for each vector space and let F be the identity on objects mapping matrices (m_ij) in the bases to (f(m_ij)).
@DiracDeltaFunk If M is compact so its homology is finitely generated, Universal Coefficent and stability of direct sums make it suffice to show that rank_R(R/pR)=rank_R(Tor(Z/p, R)). But this follows from R being integral since both sides are 0/1 iff p!=0/p=0 in R. Idk the general case.
@DiracDeltaFunk Surely you localize the monoid (as a one object category) but I don't know how to elegantly show that the canonical map is an embedding.
@DiracDeltaFunk Yrg <= or gur eryngvba qrsvarq ol k<=l vss sbe nyy bcra H, l va H vzcyvrf k va H.
Fb K vf G0 vss <= vf n cnegvny beqre naq K vf G1 vss <= vf rdhnyvgl.
Fhccbfr k<=l. Nccylvat gur ubzrbzbecuvfz t -> kt^(-1)l cerfreirf <= fb l<=k.
Urapr k=l.
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