Bibliographic record
Abstract
The invertibility hypothesis for a monoidal model category S asks that localizing an S-enriched category with respect to an equivalence results in an weakly equivalent enriched category.This is the most technical among the axioms for S to be an excellent model category in the sense of Lurie, who showed that the category Cat S of S-enriched categories then has a model structure with characterizable fibrant objects.We use a universal property of cubical sets, as a monoidal model category, to show that the invertibility hypothesis is a consequence of the other axioms.Topological categories, simplicial categories, and differential graded categories are special types of enriched categories: the enriching category has a notion of weak equivalence and its own homotopy theory.These have played a prominent role a diverse array of subjects.Getting control over the homotopy theory of some of these enriched categories and homotopical constructions in them (such as pushouts, pullbacks, and other derived limit and colimit constructions) is easier in the presence of model structures.If S is a monoidal model category, Lurie gave conditions for the existence of a model structure with many useful properties on the collection Cat S of S-enriched categories [Lur09, A.3.2.4].(In the terminology of [BM13], this allows Lurie to assert that the canonical model structure exists.)The cofibrations and weak equivalences in Cat S have a relatively straightforward description (see §2), but in order to get a useful characterization of the fibrations more assumptions are required.With this goal, Lurie defined an excellent model category as a model category S, with a symmetric monoidal structure, satisfying additional axioms labeled (A1) through (A5).The first four of these axioms are all relatively standard concepts or are straightforward to verify. Axiom (A5) is called the invertibility hypothesis.It is more technical-it roughly asserts that inverting a weak equivalence results in a weakly equivalent enriched categoryand is more difficult to verify in practice.The fact that the category Set ∆ of simplicial sets satisfies the invertibility hypothesis is an important result of Dwyer and Kan [DK80, 10.4].The invertibility hypothesis for differential graded categories is a consequence of work of Toën [Toë07, 8.7], and for enrichment in simplicial model categories it is a theorem of Dundas [Dun01, 0.9].Our main result is the following.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.002 | 0.006 |
| Open science | 0.001 | 0.005 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".