The Stacks project

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Hi French Lotto Players, I am here now Today we will upload officially French Lotto Winning Numbers. The France Lotto offers some of the best chances to win withdraws three times a weak. Find the latest winning numbers here after each game and ‘Click Here‘ button to get the full French Lotto Results a find out if you are a winner in either the main draw or the French Lotto Raffel. French Results

I think in the proof the composition $E_ i[m] \to X \to \text{hocolim} X_ n$ is supposed to be $E_ i[m] \to C \to \text{hocolim} X_ n$?

Typo in the proof of Lemma 95.19.4 : In the second to last sentence it should say "Hence $G_x \to G_y$ is an isomorphism"

trivial typo: "be homological functor" --> "be a homological functor"

I think there is a word missing in the second sentence: ...which is the sheafification of the free abelian presheaf on $\mathcal G$.

typo: 'sometime'

In the sentence "The category of super vector spaces has an internal hom which we denote $V^\vee$.", i think "internal hom" should be replaced by something like "duals".

in (2), "$Z\to Y$ is quasi-separated" should be "$Y\to X$ is quasi-separated".

I have a question concerning the material in this section. For a ring $R$ and a complex of $R$-modules $M^\bullet$ one defines the derived tensor product $- \otimes _ R^{\mathbf{L}} M^\bullet$. But I can't find any reference to a relation with the functor $F \colon K(\text{Mod}_ R) \to K(\text{Mod}_ R)$ sending $N^\bullet \mapsto \text{Tot}(N^\bullet \otimes _ R M^\bullet )$. Is it true that $LF$ is defined everywhere on $K(\text{Mod}_ R)$ in the sense of Section 13.15 (Tag 05S7) and that we have $LF = - \otimes _ R^{\mathbf{L}} M^\bullet$ as endofunctors of $D(R)$?

Small typo in part (2): It should be added "any".

I don't know if you have a standard convention about marking uses of Choice. If so, it might be worth pointing out that this argument requires Choice; see https://mathscinet.ams.org/mathscinet-getitem?mr=422022 . I ran across this page while trying to find out if Choice was needed for this Lemma, so maybe this comment will help the next person.

A potential lemma of interest here: if a module is finitely presented, then any generating set has a finite presentation. The

In the formulation of the Lemma, it is mentioned two times that the complexes $I_k^\bullet$ are K-injective (one time in the second sentence and a second time in (1)).

In LMS2, the notation doesn't make it entirely clear to me how $W$ is quantified. Maybe one wants to mention more explicitly that given $t$ and $g$ as in the diagram, there exist $W, f$ and $s$ as in the diagram (same applies to RMS2).

I think in the statement Lemma 28.44.11 you want to say that $A \rightarrow B_i$ is of finite presentation and furthermore induces a universal homeomorphism on $Spec$.

@#4333: No, this is not intentional. This is an issue which might have been caused by the server move (although it's unclear to me how), and I made a GitHub issue at https://github.com/gerby-project/gerby-website/issues/141.

I will look into it today or tomorrow. For now you can go to the section page, where for some reason the slogan is still displayed correctly.

The slogan of this tag is displayed as "None". Is this intentional?

Can sheafification be generalized to presheaves taking values in arbitrary categories (or at least a setting more general than presheaves of "nice" concrete categories)?

I think it would be good to insert the following basic lemma somewhere close to the beginning of this section.

Lemma. Any open subset of an extremally disconnected space is extremally disconnected.