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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.
@article{TAC_2024_41_a8,
author = {Guillermo Corti\~nas and Devarshi Mukherjee},
title = {A {Quillen} model structure of local homotopy equivalences},
journal = {Theory and applications of categories},
pages = {268--287},
publisher = {mathdoc},
volume = {41},
year = {2024},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TAC_2024_41_a8/}
}
Guillermo Cortiñas; Devarshi Mukherjee. A Quillen model structure of local homotopy equivalences. Theory and applications of categories, Tome 41 (2024), pp. 268-287. http://geodesic.mathdoc.fr/item/TAC_2024_41_a8/