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Record W1679869076 · doi:10.70930/tac/kvnd5iq0

A logic for categories

2010· preprint· en· W1679869076 on OpenAlexvenueno aff
Claudio Pisani

Bibliographic record

VenueTheory and applications of categories · 2010
Typepreprint
Languageen
FieldMathematics
TopicHomotopy and Cohomology in Algebraic Topology
Canadian institutionsnot available
Fundersnot available
KeywordsFunctorMathematicsCategorical variableAdjunctionContext (archaeology)Pure mathematicsSymmetry (geometry)DoctrineAlgebra over a fieldDiscrete mathematicsLawGeometry

Abstract

fetched live from OpenAlex

We present a doctrinal approach to category theory, obtained by abstracting from the indexed inclusion (via discrete fibrations and opfibrations) of left and of right actions of X ∈ Cat in categories over X. Namely, a "weak temporal doctrine" consists essentially of two indexed functors with the same codomain such that the induced functors have both left and right adjoints satisfying some exactness conditions, in the spirit of categorical logic.The derived logical rules include some adjunction-like laws involving the truth-valuesenriched hom and tensor functors, which condense several basic categorical properties and display a nice symmetry.The symmetry becomes more apparent in the slightly stronger context of "temporal doctrines", which we initially treat and which include as an instance the inclusion of lower and upper sets in the parts of a poset, as well as the inclusion of left and right actions of a graph in the graphs over it.

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)0.002
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: Methods
Teacher disagreement score0.009
Threshold uncertainty score0.031

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0020.002
Meta-epidemiology (narrow)0.0010.000
Meta-epidemiology (broad)0.0000.001
Bibliometrics0.0020.001
Science and technology studies0.0030.008
Scholarly communication0.0060.010
Open science0.0010.003
Research integrity0.0020.003
Insufficient payload (model declined to judge)0.0090.002

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 head0.026
GPT teacher head0.321
Teacher spread0.294 · 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

Citations4
Published2010
Admission routes1
Has abstractyes

Explore more

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