Galois Theory, Hopf Algebras, and Semiabelian Categories
Bibliographic record
Abstract
Algebraic cohomology: The early days by M. Barr A survey of semi-abelian categories by F. Borceux Commutator theory in regular Mal'cev categories by D. Bourn Categorical aspects of modularity by D. Bourn and M. Gran Crossed complexes and homotopy groupoids as non commutative tools for higher dimensional local-to-global problems by R. Brown Galois groupoids and covering morphisms in topos theory by M. Bunge Galois corings from the descent theory point of view by S. Caenepeel Quantum categories, star autonomy, and quantum groupoids by B. Day and R. Street Morphisms of 2-groupoids and low-dimensional cohomology of crossed modules by J. W. Duskin, R. W. Kieboom, and E. M. Vitale Applications of categorical Galois theory in universal algebra by M. Gran Fibrations for abstract multicategories by C. Hermida Lie-Rinehart algebras, descent, and quantization by J. Huebschmann A note on the semiabelian variety of Heyting semilattices by P. Johnstone Monoidal functors generated by adjunctions, with applications to transport of structure by G. M. Kelly and S. Lack On the cyclic homology of Hopf crossed products by M. Khalkhali and B. Rangipour On sequentially $h$-complete groups by G. Lukacs Embeddings of algebras by J. L. MacDonald Universal covers and category theory in polynomial and differential Galois theory by A. R. Magid Weak categories in additive 2-categories with kernels by N. Martins-Ferreira Dendrotopic sets by T. Palm On factorization systems and admissible Galois structures by A. H. Roque Hopf-Galois and bi-Galois extensions by P. Schauenburg Extension theory in Mal'tsev varieties by J. D. H. Smith On projective generators relative to coreflective classes by L. Sousa The monotone-light factorization for categories via preorders by J. J. Xarez Separable morphisms of categories via preordered sets by J. J. Xarez Frobenius algebras in tensor categories and bimodule extensions by S. Yamagami.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.006 |
| Scholarly communication | 0.004 | 0.007 |
| Open science | 0.000 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".