Definition 60.8.1. In Situation 60.7.5.

1. A divided power thickening of $X$ relative to $(S, \mathcal{I}, \gamma )$ is given by a divided power thickening $(U, T, \delta )$ over $(S, \mathcal{I}, \gamma )$ and an $S$-morphism $U \to X$.

2. A morphism of divided power thickenings of $X$ relative to $(S, \mathcal{I}, \gamma )$ is defined in the obvious manner.

The category of divided power thickenings of $X$ relative to $(S, \mathcal{I}, \gamma )$ is denoted $\text{CRIS}(X/S, \mathcal{I}, \gamma )$ or simply $\text{CRIS}(X/S)$.

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