The Stacks project

Definition 23.4.1. Given a divided power ring $(A, I, \gamma )$ and a ring map $A \to B$ we say $\gamma $ extends to $B$ if there exists a divided power structure $\bar\gamma $ on $IB$ such that $(A, I, \gamma ) \to (B, IB, \bar\gamma )$ is a homomorphism of divided power rings.

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View Definition 23.4.1 as pdf