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Record W3185759631 · doi:10.70930/tac/ndwo9npa

A practical type theory for symmetric monoidal categories

2021· article· en· W3185759631 on OpenAlexvenueno aff
Michael Shulman

Bibliographic record

VenueTheory and applications of categories · 2021
Typearticle
Languageen
FieldMathematics
TopicHomotopy and Cohomology in Algebraic Topology
Canadian institutionsnot available
FundersCarnegie Mellon University
KeywordsMathematicsSymmetric monoidal categoryMorphismType (biology)Algebra over a fieldClosed monoidal categoryPure mathematicsTensor productMonoidal categoryDomain (mathematical analysis)NotationEnriched categoryTensor (intrinsic definition)ArithmeticMathematical analysisFunctor

Abstract

fetched live from OpenAlex

We give a natural-deduction-style type theory for symmetric monoidal categories whose judgmental structure directly represents morphisms with tensor products in their codomain as well as their domain.The syntax is inspired by Sweedler notation for coalgebras, with variables associated to types in the domain and terms associated to types in the codomain, allowing types to be treated informally like "sets with elements" subject to global linearity-like restrictions.We illustrate the usefulness of this type theory with various applications to duality, traces, Frobenius monoids, and (weak) Hopf monoids. This material is based on research sponsored by The United

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)0.005
metaresearch head score (Gemma)0.004
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: none
Teacher disagreement score0.006
Threshold uncertainty score0.029

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0050.004
Meta-epidemiology (narrow)0.0010.001
Meta-epidemiology (broad)0.0010.002
Bibliometrics0.0020.001
Science and technology studies0.0020.006
Scholarly communication0.0040.011
Open science0.0020.003
Research integrity0.0020.004
Insufficient payload (model declined to judge)0.0060.002

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 head0.030
GPT teacher head0.337
Teacher spread0.307 · 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

Citations4
Published2021
Admission routes1
Has abstractyes

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