The Stacks project

Is there a typo in the wording "the obstruction to having a dimension function is an element of"? Is the obstruction itself an element of such set. If so, what is exaclty an "obstruction"? Shouldn't it be defined somewhere?

Please feel free to ignore this remark; it isn't used in what follows. The phrase "the obstruction ... element of" is not a precise mathematical statement; it is aimed at people who have heard similar phrases in the past. The statement means that given a catenary, locally Noetherian, sober topological space $X$ there is an element $o_X \in H^1(X, \mathbf{Z})$ which is zero if and only if $X$ has a dimension function. This is not a terribly useful statement in and of itself: the only thing you can deduce from this is that if $H^1(X, \mathbf{Z}) = 0$ then $X$ has a dimension function. It gets more interesting if you know how to construct $o_X$ and how it behaves: for example, given an open $U \subset X$ the image of $o_X$ in $H^1(U, \mathbf{Z})$ by the restriction map is equal to $o_U$. And so on.