The Stacks project

113.15 Obsolete lemmas on algebraic spaces

Lemmas that seem superfluous or are no longer used in the text.

Lemma 113.15.1. In Cohomology of Spaces, Situation 67.16.1 the morphism $p : X \to \mathop{\mathrm{Spec}}(A)$ is surjective.

Proof. This lemma was originally used in the proof of Cohomology of Spaces, Proposition 67.16.7 but now is a consequence of it. $\square$

Lemma 113.15.2. In Cohomology of Spaces, Situation 67.16.1 the morphism $p : X \to \mathop{\mathrm{Spec}}(A)$ is universally closed.

Proof. This lemma was originally used in the proof of Cohomology of Spaces, Proposition 67.16.7 but now is a consequence of it. $\square$


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