ScalingStacks

Proof.

Statements ([004C]) to ([004E]) are proven in [Lur17, Cor. 7.1.4.14], statement ([004F]) is an immediate consequence. Statements ([004G]) to ([004J]) can be proven analogously (and also follow from the proof of [Lur17, Lem. 5.3.2.12 (3)]). ◻