Cartan-Eilenberg created homological algebra on modules over rings. I wonder why they didn't develop it also on sheaves over ringed spaces. Grothendieck and Godement did that soon after(or almost at the same time as) the publication of the book "Homological algebra". Cartan was an expert on sheaf theory. So I think he was well aware of the possibility. I think it's strange.
2026-04-06 23:01:43.1775516503
Why didn't Cartan-Eilenberg develop homological algebra on sheaf theory?
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