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Partial corepresentations of Hopf Algebras

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Marcelo Muniz S . Alves, Eliezer Batista, Felipe Castro, Glauber Quadros, Joost Vercruysse

Rings and Algebras · Submitted 20 Nov 2019

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We prove that there exists a universal coalgebra $H^{par}$, associated to the original Hopf algebra $H$, such that the category of regular partial $H$-comodules is isomorphic to the category of $H^{par}$-comodules.

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arXiv ID1911.09141 (version 2)
Pith IDOVYGRWVT, Pith's permanent record of this paper and its review
CitationEliezer Batista, Felipe Castro, Glauber Quadros, Joost Vercruysse, Marcelo Muniz S . Alves. "Partial corepresentations of Hopf Algebras." arXiv:1911.09141 (2019). https://pith.science/paper/OVYGRWVT
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,095 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.05 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.05 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We introduce the notion of a partial corepresentation of a given Hopf algebra $H$ over a coalgebra $C$ and the closely related concept of a partial $H$-comodule. We prove that there exists a universal coalgebra $H^{par}$, associated to the original Hopf algebra $H$, such that the category of regular partial $H$-comodules is isomorphic to the category of $H^{par}$-comodules. We introduce the notion of a Hopf coalgebroid and show that the universal coalgebra $H^{par}$ has the structure of a Hopf coalgebroid over a suitable coalgebra.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We introduce the notion of a partial corepresentation of a given Hopf algebra $H$ over a coalgebra $C$ and the closely related concept of a partial $H$-comodule. contribution 1.00 0.94 0.06 asserted 0.98
s1 We prove that there exists a universal coalgebra $H^{par}$, associated to the original Hopf algebra $H$, such that the category of regular partial $H$-comodules is isomorphic to the category of $H^{par}$-comodules. result 0.95 0.96 0.65 asserted 1.00
s2 We introduce the notion of a Hopf coalgebroid and show that the universal coalgebra $H^{par}$ has the structure of a Hopf coalgebroid over a suitable coalgebra. contribution 0.71 0.95 0.22 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We introduce the notion of a partial corepresentation of a given Hopf algebra $H$ over a coalgebra $C$ and the closely related concept of a partial $H$-comodule. We prove that there exists a universal coalgebra $H^{par}$, associated to the original Hopf algebra $H$, such that the category of regular partial $H$-comodules is isomorphic to the category of $H^{par}$-comodules. We introduce the notion of a Hopf coalgebroid and show that the universal coalgebra $H^{par}$ has the structure of a Hopf coalgebroid over a suitable coalgebra.

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