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A Quillen model structure of local homotopy equivalences

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Guillermo Cortiñas, Devarshi Mukherjee

In this note, we construct a closed model structure on the category of Z/2Z-graded complexes of projective systems of ind-Banach spaces. When the base field is the fraction field F of a complete discrete valuation ring V, the homotopy category of this model category is the derived category of Z/2Z -graded complexes of the quasi-abelian category Ind(Ban_F). This homotopy category is the appropriate target of the local and analytic cyclic homology theories for complete, torsionfree V-algebras and F-algebras. When the base field is C, the homotopy category is the target of local and analytic cyclic homology for pro-bornological C-algebras, which includes the subcategory of pro-C*-algebras.

Keywords:
Model categories, cyclic homology, functional analysis

2020 MSC:
18N40, 18G35, 19D55

*Theory and Applications of Categories,*
Vol. 41, 2024,
No. 9, pp 268-287.

Published 2024-03-27.

http://www.tac.mta.ca/tac/volumes/41/9/41-09.pdf

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