Proposition 2.18 is similar to 2.19.
Why we need $N$ flat in 2.19?
What's the difference between 2.18 and 2.19?
2026-03-30 10:36:40.1774867000
Why these two propositions have different requirements
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In short, the difference is left-exactness, i.e. whether the left map is exact. Proposition 2.18 omits the $0 \longrightarrow M'$ map.