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Record W1859367190 · doi:10.70930/tac/zpxpf33n

Cyclic homology arising from adjunctions

2015· article· en· W1859367190 on OpenAlexvenueno aff
Niels Kowalzig, Ulrich Krähmer, Paul Slevin

Bibliographic record

VenueTheory and applications of categories · 2015
Typearticle
Languageen
FieldMathematics
TopicAlgebraic structures and combinatorial models
Canadian institutionsnot available
FundersEngineering and Physical Sciences Research CouncilCompagnia di San Paolo
KeywordsAdjunctionMonad (category theory)CoalgebraMorphismDistributive propertyMathematicsPure mathematicsCyclic homologyFunctorHopf algebraAssociative propertyHomology (biology)Algebra over a fieldCohomology

Abstract

fetched live from OpenAlex

Given a monad and a comonad, one obtains a distributive law between them from lifts of one through an adjunction for the other.In particular, this yields for any bialgebroid the Yetter-Drinfel'd distributive law between the comonad given by a module coalgebra and the monad given by a comodule algebra.It is this self-dual setting that reproduces the cyclic homology of associative and of Hopf algebras in the monadic framework of Bhm and S tefan.In fact, their approach generates two duplicial objects and morphisms between them which are mutual inverses if and only if the duplicial objects are cyclic.A 2-categorical perspective on the process of twisting coefficients is provided and the rle of the two notions of bimonad studied in the literature is clarified.

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 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 score0.148
Threshold uncertainty score0.285

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 head0.028
GPT teacher head0.289
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 teacher head, 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
Published2015
Admission routes1
Has abstractyes

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