An analytic Hochschild-Kostant-Rosenberg theorem

Let R be a Banach ring. We prove that the category of chain complexes complete bornological R-modules (and several related categories) is derived algebraic context in sense Raksit. then use framework algebra to version Hochschild-Kostant-Rosenberg Theorem, which relates circle action on Hochschild de Rham-differential-enriched-de Rham simplicial, commutative, algebra. This has geometric interpretation language analytic geometry, namely, loop stack equivalent shifted tangent stack. Using this we extend our results schemes.