Twisted Commutators and Internal Crossed Modules

Bo Shan Deval; Tim Van der Linden

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Twisted Commutators and Internal Crossed Modules

Bo Shan Deval, Tim Van der Linden

Category Theory · Submitted 13 Nov 2023

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

The authors' main claim We introduce a notion of relative commutator -- an important special case being commutators twisted by an action -- as a straightforward modification of the definition of the Higgins commutator, establish its relation with a new notion of commutativity -- also obtained as a modification of the usual notion -- and show how we can use it to characterise internal crossed modules in the context of a semi-abelian category.

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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, 1,706 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.02 · compares with prior results 0.39 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We introduce a notion of relative commutator -- an important special case being commutators twisted by an action -- as a straightforward modification of the definition of the Higgins commutator, establish its relation with a new notion of commutativity -- also obtained as a modification of the usual notion -- and show how we can use it to characterise internal crossed modules in the context of a semi-abelian category.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We introduce a notion of relative commutator -- an important special case being commutators twisted by an action -- as a straightforward modification of the definition of the Higgins commutator, establish its relation with a new notion of commutativity -- also obtained as a modification of the usual notion -- and show how we can use it to characterise internal crossed modules in the context of a semi-abelian category.	contribution 1.00	0.96	0.80	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.80 · evidence from proof or derivation 1.00.

What was examined, and what was not

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arXiv listing abstract v1

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P abstract

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T body sentences
C citations
R cross-paper relations

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 a notion of relative commutator -- an important special case being commutators twisted by an action -- as a straightforward modification of the definition of the Higgins commutator, establish its relation with a new notion of commutativity -- also obtained as a modification of the usual notion -- and show how we can use it to characterise internal crossed modules in the context of a semi-abelian category.

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