Bibliographic record
Abstract
Based on a study of the 2-category of weak distributive laws, we describe a method of iterating Street's weak wreath product construction.That is, for any 2-category K and for any non-negative integer n, we introduce 2-categories Wdl (n) (K), of (n + 1)-tuples of monads in K pairwise related by weak distributive laws obeying the Yang-Baxter equation.The first instance Wdl (0) (K) coincides with Mnd(K), the usual 2-category of monads in K, and for other values of n, Wdl (n) (K) contains Mnd n+1 (K) as a full 2-subcategory.For the local idempotent closure K of K, extending the multiplication of the 2-monad Mnd, we equip these 2-categories with n possible 'weak wreath product' 2-functors Wdlthat is, such that the weak wreath product is 'associative'.Whenever idempotent 2cells in K split, this leads to pseudofunctors Wdl (n) (K) → Wdl (n-1) (K) obeying the associativity property up-to isomorphism.We present a practically important occurrence of an iterated weak wreath product: the algebra of observable quantities in an Ising type quantum spin chain where the spins take their values in a dual pair of finite weak Hopf algebras.We also construct a fully faithful embedding of Wdl (n) (K) into the 2-category of commutative n + 1 dimensional cubes in Mnd(K) (hence into the 2-category of commutative n + 1 dimensional cubes in K whenever K has Eilenberg-Moore objects and its idempotent 2-cells split).Finally we give a sufficient and necessary condition on a monad in K to be isomorphic to an n-ary weak wreath product.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot 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.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.003 | 0.008 |
| Open science | 0.001 | 0.006 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
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".