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Record W2999038348 · doi:10.70930/tac/5xi8n2as

The formal theory of multimonoidal monads

2019· article· en· W2999038348 on OpenAlexvenueno aff
Gabriella Böhm

Bibliographic record

VenueTheory and applications of categories · 2019
Typearticle
Languageen
FieldMathematics
TopicHomotopy and Cohomology in Algebraic Topology
Canadian institutionsnot available
Fundersnot available
KeywordsMonad (category theory)MathematicsSymmetric monoidal categoryFunctorMonoidal categoryEnriched categoryCombinatoricsClosed monoidal categoryDiscrete mathematicsPure mathematics

Abstract

fetched live from OpenAlex

Certain aspects of Street's formal theory of monads in 2-categories are extended to multimonoidal monads in symmetric strict monoidal 2-categories.Namely, any symmetric strict monoidal 2-category M admits a symmetric strict monoidal 2category of pseudomonoids, monoidal 1-cells and monoidal 2-cells in M. Dually, there is a symmetric strict monoidal 2-category of pseudomonoids, opmonoidal 1-cells and opmonoidal 2-cells in M. Extending a construction due to Aguiar and Mahajan for M Cat, we may apply the first construction p-times and the second one q-times (in any order).It yields a 2-category M pq .A 0-cell therein is an object A of M together with p q compatible pseudomonoid structures; it is termed a pp qq-oidal object in M. A monad in M pq is called a pp, qq-oidal monad in M; it is a monad t on A in M together with p monoidal, and q opmonoidal structures in a compatible way.If M has monoidal Eilenberg-Moore construction, and certain (Linton type) stable coequalizers exist, then a pp qq-oidal structure on the Eilenberg-Moore object A t of a pp, qq-oidal monad pA, tq is shown to arise via a symmetric strict monoidal double functor to Ehresmann's double category SqrpMq of squares in M, from the double category of monads in SqrpMq in the sense of Fiore, Gambino and Kock.While q ones of the pseudomonoid structures of A t are lifted along the 'forgetful' 1-cell A t Ñ A, the other p ones are lifted along its left adjoint.In the particular example when M is an appropriate 2-subcategory of Cat, this yields a conceptually different proof of some recent results due to Aguiar, Haim and López Franco.

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)0.001
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 score0.004
Threshold uncertainty score0.015

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0020.001
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.001
Bibliometrics0.0020.001
Science and technology studies0.0010.004
Scholarly communication0.0020.005
Open science0.0010.002
Research integrity0.0010.001
Insufficient payload (model declined to judge)0.0040.001

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 head0.011
GPT teacher head0.272
Teacher spread0.261 · 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".

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Citations1
Published2019
Admission routes1
Has abstractyes

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