Geodesic
A Quillen model structure of local homotopy equivalences
Theory and applications of categories, Tome 41 (2024), pp. 268-287.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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.
Publié le :
Classification : 18N40, 18G35, 19D55
Keywords: Model categories, cyclic homology, functional analysis 
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     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/}
}
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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/