Controlled objects as a symmetric monoidal functor

Ulrich  Bunke; Luigi Caputi

doi:10.21136/HS.2022.03

Controlled objects as a symmetric monoidal functor

Ulrich Bunke^* (Corresponding Author), Luigi Caputi^* (Corresponding Author)

^*Corresponding author for this work

Mathematical Science

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Abstract

The goal of this paper is to associate functorially to every symmetric monoidal additive category A with a strict G-action a lax symmetric monoidal functor VG A : GBornCoarse → Add∞ from the symmetric monoidal category of G-bornological coarse spaces GBornCoarse to the symmetric monoidal ∞-category of additive categories Add∞. Among others, this allows to refine equivariant coarse algebraic K-homology to a lax symmetric monoidal functor.

Original language	English
Pages (from-to)	182-211
Number of pages	30
Journal	Higher Sutructures
Volume	6
Issue number	1
Early online date	1 Jul 2022
DOIs	https://doi.org/10.21136/HS.2022.03
Publication status	Published - 1 Jul 2022

Keywords

controlled objects
symmetric monoidal functors
coarse algebraic K-homology theory

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Bunke_etal_HS_Controlled_Objects_As_VoR
©Bunke and Caputi, 2022, under a Creative Commons Attribution 4.0 International License.
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Cite this

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abstract = "The goal of this paper is to associate functorially to every symmetric monoidal additive category A with a strict G-action a lax symmetric monoidal functor VG A : GBornCoarse → Add∞ from the symmetric monoidal category of G-bornological coarse spaces GBornCoarse to the symmetric monoidal ∞-category of additive categories Add∞. Among others, this allows to refine equivariant coarse algebraic K-homology to a lax symmetric monoidal functor.",

keywords = "controlled objects, symmetric monoidal functors, coarse algebraic K-homology theory",

author = "Ulrich Bunke and Luigi Caputi",

note = "Acknowledgements We thank Denis-Charles Cisinksi and Thomas Nikolaus for helpful discussion. U.B. was supported by the SFB 1085 (Higher Invariants) and L.C. was supported by the GK 1692 (Curvature, Cycles, and Cohomology).",

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AU - Caputi, Luigi

N1 - Acknowledgements We thank Denis-Charles Cisinksi and Thomas Nikolaus for helpful discussion. U.B. was supported by the SFB 1085 (Higher Invariants) and L.C. was supported by the GK 1692 (Curvature, Cycles, and Cohomology).

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N2 - The goal of this paper is to associate functorially to every symmetric monoidal additive category A with a strict G-action a lax symmetric monoidal functor VG A : GBornCoarse → Add∞ from the symmetric monoidal category of G-bornological coarse spaces GBornCoarse to the symmetric monoidal ∞-category of additive categories Add∞. Among others, this allows to refine equivariant coarse algebraic K-homology to a lax symmetric monoidal functor.

AB - The goal of this paper is to associate functorially to every symmetric monoidal additive category A with a strict G-action a lax symmetric monoidal functor VG A : GBornCoarse → Add∞ from the symmetric monoidal category of G-bornological coarse spaces GBornCoarse to the symmetric monoidal ∞-category of additive categories Add∞. Among others, this allows to refine equivariant coarse algebraic K-homology to a lax symmetric monoidal functor.

KW - controlled objects

KW - symmetric monoidal functors

KW - coarse algebraic K-homology theory

U2 - 10.21136/HS.2022.03

DO - 10.21136/HS.2022.03

M3 - Article

VL - 6

SP - 182

EP - 211

JO - Higher Sutructures

JF - Higher Sutructures

SN - 2209-0606

IS - 1

ER -

Controlled objects as a symmetric monoidal functor

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Keywords

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