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Record W1507301859 · doi:10.70930/tac/6p98o499

Compositories and Gleaves

2016· article· en· W1507301859 on OpenAlex
Cecilia Flori, T. A. Fritz

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.
fundA Canadian funder is recorded on the work.
venuePublished in a venue whose home country is Canada.

Bibliographic record

VenueTheory and applications of categories · 2016
Typearticle
Languageen
FieldMathematics
TopicAlgebraic structures and combinatorial models
Canadian institutionsPerimeter Institute
FundersMinistero dello Sviluppo EconomicoInstitut Périmètre de physique théoriqueIndustry CanadaGovernment of CanadaJohn Templeton Foundation
KeywordsMorphismMathematicsDistributive propertySheafPure mathematicsCartesian closed categoryCartesian productAlgebra over a fieldDiscrete mathematics

Abstract

fetched live from OpenAlex

Sheaves are objects of a local nature: a global section is determined by how it looks locally.Hence, a sheaf cannot describe mathematical structures which contain global or nonlocal geometric information.To fill this gap, we introduce the theory of "gleaves", which are presheaves equipped with an additional "gluing operation" of compatible pairs of local sections.This generalizes the conditional product structures of Dawid and Studen, which correspond to gleaves on distributive lattices.Our examples include the gleaf of metric spaces and the gleaf of joint probability distributions.A result of Johnstone shows that a category of gleaves can have a subobject classifier despite not being cartesian closed.Gleaves over the simplex category , which we call compositories, can be interpreted as a new kind of higher category in which the composition of an m-morphism and an n-morphism along a common k-morphism face results in an (m + n -k)-morphism.The distinctive feature of this composition operation is that the original morphisms can be recovered from the composite morphism as initial and final faces.Examples of compositories include nerves of categories and compositories of higher spans.

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.

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: Empirical
Teacher disagreement score0.059
Threshold uncertainty score0.170

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 head0.011
GPT teacher head0.264
Teacher spread0.253 · 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