Tensor product of correspondence functors

Jacques Th\'evenaz; Serge Bouc

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Tensor product of correspondence functors

Serge Bouc, Jacques Thévenaz

Representation Theory · Submitted 5 Mar 2019

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

The authors' main claim In particular, the correspondence functor associated to a finite lattice has the structure of a commutative algebra in the tensor category of all correspondence functors.

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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, 2,244 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.09 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.04 · 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.

As part of the study of correspondence functors, the present paper investigates their tensor product and proves some of its main properties. In particular, the correspondence functor associated to a finite lattice has the structure of a commutative algebra in the tensor category of all correspondence functors.

background contribution method result interpretation main claim

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	As part of the study of correspondence functors, the present paper investigates their tensor product and proves some of its main properties.	contribution 1.00	0.94	0.21	asserted 0.99
s1	In particular, the correspondence functor associated to a finite lattice has the structure of a commutative algebra in the tensor category of all correspondence functors.	result 1.00	0.83	0.45	asserted 1.00

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

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arXiv listing abstract v1

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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

As part of the study of correspondence functors, the present paper investigates their tensor product and proves some of its main properties. In particular, the correspondence functor associated to a finite lattice has the structure of a commutative algebra in the tensor category of all correspondence functors.

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What this paper does with the arXiv papers it cites

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

What it cites · 3 sentences without a confident label

Cites as background 1 paper

In recent papers [ref] , we developed the theory of correspondence functors, namely functors from the category $$ of finite sets and correspondences to the category $k-$ of all $k$-modules, where $k$ is a commutative ring.

The algebra of Boolean matrices, correspondence functors, and simplicity · Introduction · 0.93

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