The Stacks project

Situation 15.6.1. In the following we will consider ring maps

\[ \xymatrix{ B \ar[r] & A & A' \ar[l] } \]

where we assume $A' \to A$ is surjective with kernel $I$. In this situation we set $B' = B \times _ A A'$ to obtain a cartesian square

\[ \xymatrix{ A & A' \ar[l] \\ B \ar[u] & B' \ar[l] \ar[u] } \]

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View Situation 15.6.1 as pdf