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\begin{equation*} \DeclareMathOperator\Coim{Coim} \DeclareMathOperator\Coker{Coker} \DeclareMathOperator\Ext{Ext} \DeclareMathOperator\Hom{Hom} \DeclareMathOperator\Im{Im} \DeclareMathOperator\Ker{Ker} \DeclareMathOperator\Mor{Mor} \DeclareMathOperator\Ob{Ob} \DeclareMathOperator\Sh{Sh} \DeclareMathOperator\SheafExt{\mathcal{E}\mathit{xt}} \DeclareMathOperator\SheafHom{\mathcal{H}\mathit{om}} \DeclareMathOperator\Spec{Spec} \newcommand\colim{\mathop{\mathrm{colim}}\nolimits} \newcommand\lim{\mathop{\mathrm{lim}}\nolimits} \newcommand\Qcoh{\mathit{Qcoh}} \newcommand\Sch{\mathit{Sch}} \newcommand\QCohstack{\mathcal{QC}\!\mathit{oh}} \newcommand\Cohstack{\mathcal{C}\!\mathit{oh}} \newcommand\Spacesstack{\mathcal{S}\!\mathit{paces}} \newcommand\Quotfunctor{\mathrm{Quot}} \newcommand\Hilbfunctor{\mathrm{Hilb}} \newcommand\Curvesstack{\mathcal{C}\!\mathit{urves}} \newcommand\Polarizedstack{\mathcal{P}\!\mathit{olarized}} \newcommand\Complexesstack{\mathcal{C}\!\mathit{omplexes}} \newcommand\Pic{\mathop{\mathrm{Pic}}\nolimits} \newcommand\Picardstack{\mathcal{P}\!\mathit{ic}} \newcommand\Picardfunctor{\mathrm{Pic}} \newcommand\Deformationcategory{\mathcal{D}\!\mathit{ef}} \end{equation*}

On left comment #10353 on Section 6.6 in Sheaves on Spaces

Should "tensor product presheaf" be in italics?


On m left comment #10352 on Section 5.26 in Topology

Consider the following map of finite topological spaces, hopefully in suggestive notation:

Here denotes the disjoint union, the subscripts indicate where each point goes, and means that point lies in the closure of point .

Then we can add the following item to Proposition 5.26.6(08YN). I state it in full:

Proposition 5.26.6' (08YN'). Let X be a topological space. The following are equivalent (1) X is extremally disconnected, (2) for any solid commutative diagram of continuous maps with the surjective proper map of finite topological spaces defined above, there is a dotted arrow in the category of topological spaces making the diagram commute.

Proof. It is clear that (1) implies (2). On the other hand, if (2) holds, for an open subset of consider the map where is the preimage of , and is the preimage of . Continuity of the lifting is then equivalent to the closure of being open.


On ZL left comment #10351 on Lemma 13.36.5 in Derived Categories

Sorry I missed that "generator" and "weak generator" are the same thing defined in Definition 13.36.3. In this situation, when you say " generates " do you mean that is a weak generator of ?


On left comment #10350 on Lemma 13.20.1 in Derived Categories

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On Davide Pierrat left comment #10349 on Lemma 6.20.1 in Sheaves on Spaces

"Let be a presheaf -modules" should be "Let be a presheaf of -modules".


On ZL left comment #10348 on Lemma 13.36.5 in Derived Categories

A search using either "generator" or "generators" did not show the definition of generator before this Lemma. By "generator" do you mean the generator defined in Section 19.10 ?


On left comment #10347 on Section 60.7 in Crystalline Cohomology

Sorry, but now I cannot understand which lemma this refers to. Please use tags when referring to things OR (preferable) comment on the page of the tag you are talking about.


On left comment #10346 on Lemma 15.114.8 in More on Algebra

Thanks to you both. Fixed here.


On left comment #10345 on Lemma 13.13.8 in Derived Categories

Thanks, fixed here.


On left comment #10344 on Lemma 10.99.4 in Commutative Algebra

Indeed. FIxed here.


On left comment #10343 on Section 88.30 in Algebraization of Formal Spaces

Oops. Added here.


On left comment #10342 on Lemma 36.22.5 in Derived Categories of Schemes

OK, I changed this here.


On left comment #10341 on Lemma 42.67.5 in Chow Homology and Chern Classes

Thanks. Fixed here.


On left comment #10340 on Lemma 13.14.5 in Derived Categories

Going to leave as is.


On nkym left comment #10339 on Lemma 12.19.10 in Homological Algebra

The last ) in the proof I think is redundant


On m left comment #10338 on Section 5.26 in Topology

Consider the following map of finite topological spaces, hopefully in suggestive notation:

Here denotes the disjoint union, the subscripts indicate where each point goes, and means that point lies in the closure of point .

Then we can add the following item to Proposition 5.26.6(08YN). I state it in full:

Proposition 5.26.6' (08YN'). Let X be a topological space. The following are equivalent

X is extremally disconnected,


for any solid commutative diagram $X \longrightarrow Z_0 \xleftarrow \pi Y_0$
of continuous maps with the surjective proper map $\pi:Y_0\longrightarrow Z_0$ of finite topological spaces defined above,  there is a dotted arrow $X\longrightarrow Y_0$ in the category of topological spaces making the diagram commute.

Proof. It is clear that (1) implies (2). On the other hand, if (2) holds, for an open subset of consider the map where is the preimage of , and is the preimage of . Continuity of the lifting is then equivalent to the closure of being open.


On left comment #10337 on Item 50

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On Anonymous left comment #10336 on Lemma 94.10.10 in Algebraic Stacks

Sure - I was just trying to say that Lemma 4.35.9 implies something slightly stronger, after the present lemma is proved. And as for the reference to Lemma 100.8.4, I think I was trying to say that the proof idea in loc. cit. would give a shorter proof of the present lemma (though I have since forgotten whether the proofs might be mostly the same anyways).

(Feel free to ignore this comment.)


On left comment #10335 on Definition 13.14.2 in Derived Categories

Going to leave as is.


On left comment #10334 on Remark 4.22.4 in Categories

Thanks Elias. Going to leave this as is for now.