I am confused with lemma 25.13.3. Especially with the equivalence.
At -2 lines of lemma 25.13.3 , the author writes,
Given any set of extensions $\kappa \subseteq K_i$ there exists some field extension of $\kappa \subseteq \Omega$ such that all the field extensions $K_i$ are contained in the extension $\Omega$.
Does this not imply that we have an $\Omega$ completing the diagram at -3 lines for any $K,L$?
Hence $p:Spec(K) \rightarrow X, q:Spec(L) \rightarrow X$ are equivalent for any choice of $K,L$ given that they have the same image? It seems to me that this equivalence is unnecessary...