Globalizations for partial (co)actions on coalgebras

Felipe Castro; Glauber Quadros

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Globalizations for partial (co)actions on coalgebras

Felipe Castro, Glauber Quadros

Rings and Algebras · Submitted 5 Oct 2015

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

The authors' main claim We show that every partial module coalgebra is globalizable exhibiting a standard globalization.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,547 input tokens.

What the abstract itself states, as probabilities: claims first 0.08 · states limitation 0.82 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.76 · mentions code or data availability 0.02.

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

In this paper, we introduce the notion of globalization for partial module coalgebra and for partial comodule coalgebra. We show that every partial module coalgebra is globalizable exhibiting a standard globalization. We also show the existence of globalization for a partial comodule coalgebra, provided a certain rationality condition. Moreover, we show a relationship between the globalization for the (co)module coalgebra and the usual globalization for the (co)module algebra.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	In this paper, we introduce the notion of globalization for partial module coalgebra and for partial comodule coalgebra.	contribution 1.00	0.91	0.12	asserted 0.99
s1	We show that every partial module coalgebra is globalizable exhibiting a standard globalization.	result 0.96	0.96	0.35	asserted 1.00
s2	We also show the existence of globalization for a partial comodule coalgebra, provided a certain rationality condition.	result 0.94	0.94	0.15	asserted 0.99
s3	Moreover, we show a relationship between the globalization for the (co)module coalgebra and the usual globalization for the (co)module algebra.	result 0.89	0.93	0.14	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.96 · evidence from proof or derivation 1.00.

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arXiv listing abstract v2

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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

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Original abstract

In this paper, we introduce the notion of globalization for partial module coalgebra and for partial comodule coalgebra. We show that every partial module coalgebra is globalizable exhibiting a standard globalization. We also show the existence of globalization for a partial comodule coalgebra, provided a certain rationality condition. Moreover, we show a relationship between the globalization for the (co)module coalgebra and the usual globalization for the (co)module algebra.

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6 arXiv papers cite this in 13 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 6 sentences without a confident label

Builds on it 2 papers

Our purpose in this section is to generalize the dualization results presented in [ref] for the case of weak Hopf algebras.

Partial Actions of Weak Hopf Algebras on Coalgebras · Dualization · 1.00
Quadros in [ref] , we will make the analogue for partial module algebras in the context of multiplier Hopf algebras in order to construct a globalization for these structures.

Multiplier Hopf Algebras: Globalization for partial actions · Induced Partial Module Algebra · 0.93

Cites it as background 4 papers

More details can be found in [ref] , [ref] and [ref] .

Partial Actions of Weak Hopf Algebras on Coalgebras · Partial Actions on Algebras · 0.99
[ref] Let $H$ be a Hopf algebra, $z∈H$ and $C$ a counital coalgebra.

Hopf algebras arising from partial (co)actions · Partial (co)actions · 0.90
More generally the problem was investigated for partial semigroup actions in [ref] , for partial groupoid actions in [ref] and around partial Hopf (co)actions in [ref] .

Globalization of partial cohomology of groups · Introduction · 0.93

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