The Stacks project

Lemma 109.79.1. There exists a ring $A$ and an infinite family of flat ring maps $\{ A \to A_ i\} _{i \in I}$ such that for every $A$-module $M$

\[ M = \text{Equalizer}\left( \xymatrix{ \prod \nolimits _{i \in I} M \otimes _ A A_ i \ar@<1ex>[r] \ar@<-1ex>[r] & \prod \nolimits _{i, j \in I} M \otimes _ A A_ i \otimes _ A A_ j } \right) \]

but there is no finite subfamily where the same thing is true.

Proof. See discussion above. $\square$


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