Homotopy linear algebra

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Standard

Homotopy linear algebra. / Galvez-Carrillo, Imma; Kock, Joachim; Tonks, Andrew.

In: Proceedings of the Royal Society of Edinburgh Section A: Mathematics, Vol. 148, No. 2, 04.2018, p. 293-325.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Galvez-Carrillo, I, Kock, J & Tonks, A 2018, 'Homotopy linear algebra', Proceedings of the Royal Society of Edinburgh Section A: Mathematics, vol. 148, no. 2, pp. 293-325. https://doi.org/10.1017/S0308210517000208

APA

Galvez-Carrillo, I., Kock, J., & Tonks, A. (2018). Homotopy linear algebra. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 148(2), 293-325. https://doi.org/10.1017/S0308210517000208

Vancouver

Galvez-Carrillo I, Kock J, Tonks A. Homotopy linear algebra. Proceedings of the Royal Society of Edinburgh Section A: Mathematics. 2018 Apr;148(2):293-325. https://doi.org/10.1017/S0308210517000208

Author

Galvez-Carrillo, Imma ; Kock, Joachim ; Tonks, Andrew. / Homotopy linear algebra. In: Proceedings of the Royal Society of Edinburgh Section A: Mathematics. 2018 ; Vol. 148, No. 2. pp. 293-325.

Bibtex

@article{07a0e03d74db401c955d93364b90d424,
title = "Homotopy linear algebra",
abstract = "By homotopy linear algebra we mean the study of linear functors between slices of the infinity-category of infinity-groupoids, subject to certain finiteness conditions. After some standard definitions and results, we assemble said slices into infinity-categories to model the duality between vector spaces and profinite-dimensional vector spaces, and set up a global notion of homotopy cardinality a la Baez, Hoffnung and Walker compatible with this duality. We needed these results to support our work on incidence algebras and Mobius inversion over infinity-groupoids; we hope that they can also be of independent interest.",
keywords = "infinity-groupoids, homotopy cardinality, homotopy finiteness, duality, linear algebra",
author = "Imma Galvez-Carrillo and Joachim Kock and Andrew Tonks",
year = "2018",
month = apr,
doi = "10.1017/S0308210517000208",
language = "English",
volume = "148",
pages = "293--325",
journal = "Proceedings of the Royal Society of Edinburgh Section A: Mathematics",
issn = "0308-2105",
publisher = "The/R S E Scotland Foundation",
number = "2",

}

RIS

TY - JOUR

T1 - Homotopy linear algebra

AU - Galvez-Carrillo, Imma

AU - Kock, Joachim

AU - Tonks, Andrew

PY - 2018/4

Y1 - 2018/4

N2 - By homotopy linear algebra we mean the study of linear functors between slices of the infinity-category of infinity-groupoids, subject to certain finiteness conditions. After some standard definitions and results, we assemble said slices into infinity-categories to model the duality between vector spaces and profinite-dimensional vector spaces, and set up a global notion of homotopy cardinality a la Baez, Hoffnung and Walker compatible with this duality. We needed these results to support our work on incidence algebras and Mobius inversion over infinity-groupoids; we hope that they can also be of independent interest.

AB - By homotopy linear algebra we mean the study of linear functors between slices of the infinity-category of infinity-groupoids, subject to certain finiteness conditions. After some standard definitions and results, we assemble said slices into infinity-categories to model the duality between vector spaces and profinite-dimensional vector spaces, and set up a global notion of homotopy cardinality a la Baez, Hoffnung and Walker compatible with this duality. We needed these results to support our work on incidence algebras and Mobius inversion over infinity-groupoids; we hope that they can also be of independent interest.

KW - infinity-groupoids

KW - homotopy cardinality

KW - homotopy finiteness

KW - duality

KW - linear algebra

U2 - 10.1017/S0308210517000208

DO - 10.1017/S0308210517000208

M3 - Journal article

VL - 148

SP - 293

EP - 325

JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

SN - 0308-2105

IS - 2

ER -

ID: 331498191