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

University of Regensburg

Research output: Contribution to journal › Article › peer-review

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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

Bibliographical 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).

Keywords

controlled objects
symmetric monoidal functors
coarse algebraic K-homology theory

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Bunke_etal_HS_Controlled_Objects_As_VoR
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Cite this

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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

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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

SN - 2209-0606

VL - 6

SP - 182

EP - 211

JO - Higher Sutructures

JF - Higher Sutructures

IS - 1

ER -

Controlled objects as a symmetric monoidal functor

Abstract

Bibliographical note

Keywords

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