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Comments 541 to 560 out of 9050 in reverse chronological order.

\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 #9179 on Definition 50.15.1 in de Rham Cohomology

No! The sentence already says "for all in " and we really want this to be true for all . Maybe I misunderstood your comment?

On left comment #9178 on Section 22.26 in Differential Graded Algebra

The endomorphism ring of an object in a linear category, resp. graded category, resp. differential graded category is an -algebra, resp. graded -algebra, resp. differential graded -algebra. The things you mention are properties of such algebras. Conventions on algebras in this chapter are in Section 22.2.

On left comment #9177 on Lemma 10.138.14 in Commutative Algebra

Good catch! Thanks and fixed here.

On left comment #9176 on Lemma 37.53.1 in More on Morphisms

Thanks and fixed here.

On left comment #9175 on Section 15.78 in More on Algebra

@#8833: the union is a colimit so the lemma applies.

@#9174: The sum is finite in each degree because for . The reason this is important is because otherwise there wouldn't be a map from into the direct sum! Of course the direct sum itself (in the derived category) is not finite and to conclude we use the compactness of in the next sentence: "By assumption..." So it seems fine to me.

On Sergey Guminov left comment #9174 on Section 15.78 in More on Algebra

I don't understand the phrase "This makes sense as in each degree the direct sum on the right is finite." in the proof of Proposition 07LT. I don't see any a priori reason why this sum would be finite. I think one should use the compactness of at this moment to see that it's enough to define maps to each summand to get a map to the whole sum.

On left comment #9173 on Section 19.6 in Injectives

Thanks and fixed here.

On left comment #9172 on Lemma 30.4.4 in Cohomology of Schemes

Oops! Indeed, terrible! I have fixed this here.

On left comment #9171 on Section 9.13 in Fields

You absolutely need a monoid to have a unit element and homomorphisms of monoids need to send unit to unit otherwise this thing is wrong (since otherwise all of could be mapped to in the field).

On left comment #9170 on Section 19.11 in Injectives

@#8602: Yes, you are correct. However when we use the phrase Grothendieck abelian category we typically mean a "big" one and should be on the list. So strictly speaking, in the definitions, lemmas, propositions, theorems, and remarks of Sections 19.10, 19.11, 19.12, 19.13, 19.14, and 19.15 should mention the "bigness" as we did correctly for example in Categories, Section 4.25.

Maybe we can leave this alone for now and the reader can assume that a lemma or such discussing Grothendieck abelian categories is one about a suitable "big" category.

Please discuss!

On left comment #9169 on Lemma 7.30.6 in Sites and Sheaves

Thanks and fixed here.

On left comment #9168 on Section 29.47 in Morphisms of Schemes

Thanks and fixed here.

On left comment #9167 on Lemma 19.12.3 in Injectives

Thanks and fixed here.

On left comment #9166 on Lemma 36.13.5 in Derived Categories of Schemes

Thanks and fixed here.

On left comment #9165 on Section 6.7 in Sheaves on Spaces

No problem and I enjoy working on this!

On left comment #9164 on Lemma 19.12.2 in Injectives

I am always in favor or changes to decrease the total number of characters while preserving the content of the text! Change here.

On left comment #9163 on Section 66.16 in Properties of Algebraic Spaces

Thanks and fixed here.

On left comment #9162 on Lemma 36.22.5 in Derived Categories of Schemes

OK, I added a reference here but I wonder if this makes it less readable.

On left comment #9161 on Example 68.13.11 in Decent Algebraic Spaces

Thanks and fixed here.

On left comment #9160 on Lemma 29.43.16 in Morphisms of Schemes

Thanks and fixed here.


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