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Record W2143354333 · doi:10.70930/tac/j56g20b6

Notes on enriched categories with colimits of some class

2005· article· en· W2143354333 on OpenAlexvenueno aff
G. M. Kelly, Victor Schmitt

Bibliographic record

VenueTheory and applications of categories · 2005
Typearticle
Languageen
FieldMathematics
TopicHomotopy and Cohomology in Algebraic Topology
Canadian institutionsnot available
FundersEngineering and Physical Sciences Research Council
KeywordsMathematicsBase (topology)Class (philosophy)Equivalence (formal languages)CombinatoricsPure mathematicsComputer scienceMathematical analysisArtificial intelligence

Abstract

fetched live from OpenAlex

The paper is in essence a survey of categories having φ-weighted colimits for all the weights φ in some class Φ.We introduce the class Φ + of Φ-flat weights which are those ψ for which ψ-colimits commute in the base V with limits having weights in Φ; and the class Φ -of Φ-atomic weights, which are those ψ for which ψ-limits commute in the base V with colimits having weights in Φ.We show that both these classes are saturated (that is, what was called closed in the terminology of [AK88]).We prove that for the class P of all weights, the classes P + and P -both coincide with the class Q of absolute weights.For any class Φ and any category A, we have the free Φ-cocompletion Φ(A) of A; and we recognize Q(A) as the Cauchy-completion of A. We study the equivalence between (Q(A op ))op and Q(A), which we exhibit as the restriction of the Isbell adjunction between [A, V] op and [A op , V] when A is small; and we give a new Morita theorem for any class Φ containing Q.We end with the study of Φ-continuous weights and their relation to the Φ-flat weights.

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 imitation

Not 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.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.002
Version: metacan-v3-hybrid-931329e0061cValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.006
Threshold uncertainty score0.020

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0010.002
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.001
Bibliometrics0.0040.004
Science and technology studies0.0020.004
Scholarly communication0.0030.009
Open science0.0010.003
Research integrity0.0010.002
Insufficient payload (model declined to judge)0.0060.000

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.

Opus teacher head0.016
GPT teacher head0.280
Teacher spread0.265 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it

Classification

machine, unvalidated

Machine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
Study designTheoretical or conceptual
Domainnot available
GenreEmpirical

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".

Quick stats

Citations81
Published2005
Admission routes1
Has abstractyes

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