standOff, and the article is at its publisher via the link below. When we have changed our mind. Some entries in the table begin with a word in capitals and the reason for it. EVIDENCE CORRECTED — the finding still stands, but we had quoted the wrong sentence from the paper, and the quotation has been replaced with the right one. RETRACTED — the entry itself was wrong; it stays on the page, marked, with the reason, rather than being deleted. WITHDRAWN AND REPLACED — the entry was wrong, and a corrected version of it appears in the entries below. Each mark carries its own reason, in brackets, because the reasons differ from one entry to the next. An entry we have WITHDRAWN is removed from this page and kept in the record, with its reason. A line reading Audit and a date is a later re-reading of the entry against its whole sentence: DOUBTFUL means it was kept, and the reason says what is loose about it. Quotation marks inside the tagger's sentence. Where a tag is the tagger's own sentence, a phrase in quotation marks inside it is borrowed from the paper — the tagger's wording around it is not. The paper's own sentence is the evidence quote for that row; on this page it is withheld with the article, and the article is at its publisher. Nothing inside quotation marks anywhere on this page is ours: if it is quoted, it is the paper's. Whose words a concept carries. A concept entry records a term the paper itself uses, so the term, the sense given for it, and its evidence are the paper's own words, quoted where the paper fixes them. This is the opposite of a sense entry in the tag table, which is the tagger's sentence about how the paper uses a term. Where a concept entry could not be grounded in the paper's words, the entry says so on its own row.| relation to other work | claim_relations | how this paper stands to another: agrees, contradicts, extends, qualifies |
| claim type | claim_type | the shape of the claim: existence, mechanism, method, critique, prediction, null |
| concept edge | concept_edges | an asserted relation between two concepts, with the sentence asserting it |
| concept | concepts | an idea the paper works with, quoted where the paper uses it |
| content tag | content_tags | a finding, definition, quantity, statistic or variable named in the paper |
| limitation | limitations | what the paper says its evidence cannot support |
| mechanism | mechanisms | how the reported effect is said to come about |
| method | method | how the paper produced its evidence |
| phenomenon | phenomenon | the effect or regularity under study |
| sense | senses | a distinct use of a term, quoted where the paper fixes it |
Relations on this page carry a quotation for the claim. Where a relation was separately evidenced — and so tested against the vocabulary for its type — the row says so; none of 1 relation here carry that mark. The rest are the tagger’s reading of the sentence quoted beside them.
This record holds no controls. A layer is empty when the tagger recorded nothing in it — which is not the same as the paper having nothing to record.
| facet | tag | field | conf. | whose words |
|---|---|---|---|---|
| claim_type | existence Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | claim_type | the paper's words | |
| phenomenon | descent for sheaves on compact Hausdorff spaces Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | phenomenon | the paper's words | |
| method | mathematical-proof Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: mathematical-proof | method | the paper's words | |
| mechanisms | mechanisms Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | mechanisms[0] | the tagger's words | |
| limitations | The descent and full-faithfulness results fail before Postnikov completion; the paper devotes sections to explaining why. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | limitations[0] | the tagger's words | |
| limitations | Whether every-object-is-the-limit-of-its-Postnikov-tower is strictly weaker than Postnikov completeness is left open. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | limitations[1] | the tagger's words | |
| limitations | The protruncated shape, one of the derived consequences, does not preserve pullbacks. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | limitations[2] | the tagger's words | |
| limitations | Three competing sheaf theories agree on all truncated objects, so which one a result used is invisible until unbounded objects are involved. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: a result stated for sheaves on a space: sheaves, hypersheaves and Postnikov complete sheaves all have the same truncated objects, and the differences between the three theories appear only on unbounded objects - so two such results can be compared safely in the truncated case and not otherwise | limitations[3] | 1.0 | the tagger's words |
| limitations | Two incompatible set-theoretic foundations are in use in this literature; the difference is declared inessential and then not mentioned again. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: a comparison between results in this paper and results of Clausen and Scholze: the two use different set-theoretic foundations, one with universes and one avoiding them, which the author states is a minor difference not affecting any argument in an essential way | limitations[4] | 1.0 | the tagger's words |
| limitations | The agreement between three cohomology theories is claimed for spaces satisfying a stated structural condition, not in general. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: the claim that condensed and sheaf cohomology agree: the three-way agreement is asserted for a topological space admitting a locally finite CW structure, so it is a conditional identification rather than a general one | limitations[5] | 1.0 | the tagger's words |
| concepts | hypersheaves Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: hypersheaves | concepts[0] | the paper's words | |
| concepts | Postnikov complete sheaves Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: Postnikov complete sheaves | concepts[1] | the paper's words | |
| concepts | condensed cohomology Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: condensed cohomology | concepts[2] | the paper's words | |
| concepts | compact Hausdorff spaces Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: compact Hausdorff spaces | concepts[3] | the paper's words | |
| concepts | hypercompleteness Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: hypercompleteness | concepts[4] | the paper's words | |
| senses | sheaf theory - THREE OF THEM, DISTINGUISHED ONLY OFF THE TRUNCATED PART: sheaves, hypersheaves and Postnikov complete sheaves all extend the classical theory and share their truncated objects, so the choice between them is undetectable in the bounded case Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | senses[0] | 1.0 | the tagger's words |
| senses | the subject's name - CONDENSED/PYKNOTIC, BOTH CARRIED: the field is written with a slash between two names for it, in a paper by one of the pyknotic authors thanking the condensed ones Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | senses[1] | 1.0 | the tagger's words |
| senses | the set theory - A DIFFERENCE DECLARED AND THEN SET ASIDE: universes here, no universes there, and an explicit decision not to mention it again Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | senses[2] | 1.0 | the tagger's words |
| claim_relations | extends → Dyckhoff [7, Theorem 3.11; 8] and Clausen–Scholze [23, Theorem 3.2] comparison of sheaf and condensed cohomology Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | claim_relations[0] | the tagger's words | |
| claim_relations | builds-on → Clausen–Scholze's condensed/pyknotic mathematics, Barwick–Haine, and Lurie's work on ultracategories Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | claim_relations[1] | the tagger's words | |
| concept_edges | Postnikov complete sheaves —distinct-from→ hypersheaves Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. strength of the relation: 1 also in: Postnikov complete sheaves · hypersheaves | concept_edges[0] | the tagger's words | |
| content_tags | For a compactly assembled coefficient ∞-category, the assignment of the ∞-category of Postnikov complete sheaves to a locally compact Hausdorff space satisfies descent along proper surjections. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[0] | the tagger's words | |
| content_tags | The same result gives proper descent for left complete derived ∞-categories and shows that Postnikov complete sheaves form a sheaf on compact Hausdorff spaces for the topology of finite jointly surjective families. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[1] | the tagger's words | |
| content_tags | Neither ordinary sheaves nor hypersheaves define a sheaf on the site of compact Hausdorff spaces. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[2] | the tagger's words | |
| content_tags | Postnikov complete sheaves on a locally compact Hausdorff space embed fully faithfully into condensed objects over that space. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[3] | the tagger's words | |
| content_tags | Consequently the sheaf cohomology and the condensed cohomology of a locally compact Hausdorff space coincide. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[4] | the tagger's words | |
| content_tags | For a space carrying a locally finite CW structure, condensed, singular and sheaf cohomology all coincide. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[5] | the tagger's words | |
| content_tags | Sheaves on a profinite set are Postnikov complete, whereas sheaves on the Hilbert cube are not, so Postnikov completeness is not automatic for compact Hausdorff spaces. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[6] | the tagger's words | |
| content_tags | The protruncated shape functor fails to preserve pullbacks of compact Hausdorff spaces. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. | content_tags.findings[7] | the tagger's words | |
| content_tags | Postnikov completion Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: Postnikov completion | content_tags.definitions[0] | the tagger's words | |
| content_tags | Postnikov complete Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: Postnikov complete | content_tags.definitions[1] | the tagger's words | |
| content_tags | proper descent Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: proper descent | content_tags.definitions[2] | the tagger's words | |
| content_tags | compactly assembled ∞-category Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: compactly assembled ∞-category | content_tags.definitions[3] | the tagger's words | |
| content_tags | hypercomplete objects Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: hypercomplete objects | content_tags.definitions[4] | the tagger's words | |
| content_tags | van Kampen colimit Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: van Kampen colimit | content_tags.definitions[5] | the tagger's words | |
| content_tags | Postnikov complete sheaves Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: Postnikov complete sheaves | content_tags.definitions[6] | the tagger's words |
Tags that could not be placed in the text:
What was deliberately not tagged, and why, is recorded per paper by the tagger. Where a paper has no such record, this page says so rather than implying that nothing was declined.