Quasi-coherent sheaves in differential geometry

It is proved that the category of simplicial complete bornological spaces over \(\mathbb R\) carries a combinatorial monoidal model structure satisfying the monoid axiom. For any commutative monoid in this category the category of modules is also a monoidal model category with all cofibrant objects...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2017-07
Main Authors: Borisov, Dennis, Kremnizer, Kobi
Format: Article
Language:English
Subjects:
Combinatorial analysis
Differential geometry
Equivalence
Modules
Monoids
Sheaves
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:It is proved that the category of simplicial complete bornological spaces over \(\mathbb R\) carries a combinatorial monoidal model structure satisfying the monoid axiom. For any commutative monoid in this category the category of modules is also a monoidal model category with all cofibrant objects being flat. In particular, weak equivalences between these monoids induce Quillen equivalences between the corresponding categories of modules. On the other hand, it is also proved that the functor of pre-compact bornology applied to simplicial \(C^\infty\)-rings preserves and reflects weak equivalences, thus assigning stable model categories of modules to simplicial \(C^\infty\)-rings.
ISSN:2331-8422