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Record W4413966187 · doi:10.70930/tac/z2jgorg4

Quotients of unital A_∞-categories

2008· article· en· W4413966187 on OpenAlexvenueno aff
Volodymyr Lyubashenko, Oleksandr Manzyuk

Bibliographic record

VenueTheory and applications of categories · 2008
Typearticle
Languageen
FieldMathematics
TopicHomotopy and Cohomology in Algebraic Topology
Canadian institutionsnot available
Fundersnot available
KeywordsUnitalQuotientMathematicsPure mathematicsAlgebra over a field

Abstract

fetched live from OpenAlex

Assuming that B is a full A ∞ -subcategory of a unital A ∞ -category C we construct the quotient unital A ∞ -category D ='C/B'.It represents the A u ∞ -2-functor A → A u ∞ (C, A) mod B , which associates with a given unital A ∞ -category A the A ∞ -category of unital A ∞ -functors C → A, whose restriction to B is contractible.Namely, there is a unital A ∞ -functor e : C → D such that the composition B ↩→ C e -→ D is contractible, and for an arbitrary unital A ∞ -category A the restriction A ∞ -functor (e 1)M :is an equivalence.Let C k be the differential graded category of differential graded k-modules.We prove that the Yoneda A ∞ -functor Y : A → A u ∞ (A op , C k ) is a full embedding for an arbitrary unital A ∞ -category A. In particular, such A is A ∞ -equivalent to a differential graded category with the same set of objects.

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: Methods · Consensus signal: none
Teacher disagreement score0.006
Threshold uncertainty score0.019

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0010.002
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0020.001
Science and technology studies0.0010.003
Scholarly communication0.0020.004
Open science0.0010.003
Research integrity0.0000.001
Insufficient payload (model declined to judge)0.0060.001

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 head0.020
GPT teacher head0.282
Teacher spread0.262 · 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
GenreMethods

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

Citations0
Published2008
Admission routes1
Has abstractyes

Explore more

Same venueTheory and applications of categoriesSame topicHomotopy and Cohomology in Algebraic TopologyFrench-language works237,207