MétaCan
Menu
Back to cohort
Record W4413966281 · doi:10.70930/tac/51kvc0xu

Internal monotone-light factorization for categories via preorders

2004· article· en· W4413966281 on OpenAlexvenueno aff
João J. Xarez

Bibliographic record

VenueTheory and applications of categories · 2004
Typearticle
Languageen
FieldMathematics
TopicAdvanced Topics in Algebra
Canadian institutionsnot available
Fundersnot available
KeywordsMonotone polygonFactorizationMathematicsComputer scienceAlgebra over a fieldPure mathematicsAlgorithmGeometry

Abstract

fetched live from OpenAlex

It is shown that, for a finitely-complete category C with coequalizers of kernel pairs, if every product-regular epi is also stably-regular then there exist the reflections (R)Grphs(C) (R)Rel(C), from (reflexive) graphs into (reflexive) relations in C, and Cat(C) Preord(C), from categories into preorders in C. Furthermore, such a sufficient condition ensures as well that these reflections do have stable units.This last property is equivalent to the existence of a monotone-light factorization system, provided there are sufficiently many effective descent morphisms with domain in the respective full subcategory.In this way, we have internalized the monotone-light factorization for small categories via preordered sets, associated with the reflection Cat Preord, which is now just the special case C = Set.

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 distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation 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: none
Teacher disagreement score0.953
Threshold uncertainty score0.502

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

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 head0.015
GPT teacher head0.299
Teacher spread0.284 · 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 teacher head, 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

Citations1
Published2004
Admission routes1
Has abstractyes

Explore more

Same venueTheory and applications of categoriesSame topicAdvanced Topics in AlgebraFrench-language works237,207