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dc.rights.licenseCC-BY-NC-ND
dc.contributor.advisorSchreiber, Dr. Urs
dc.contributor.advisorMoerdijk, Prof. dr. I.
dc.contributor.authorStel, H.G.
dc.date.accessioned2011-03-29T17:00:51Z
dc.date.available2011-03-29
dc.date.available2011-03-29T17:00:51Z
dc.date.issued2011
dc.identifier.urihttps://studenttheses.uu.nl/handle/20.500.12932/6822
dc.description.abstractFor T any abelian Lawvere theory, we establish a Quillen adjunction between model category structures on cosimplicial T-algebras and on simplicial presheaves over duals of T-algebras, whose left adjoint forms algebras of functions with values in the canonical T-line object. We find mild general conditions under which this descends to the local model structure that models ∞-stacks over duals of T-algebras. For T the theory of commutative algebras this reproduces the situation in Toën's Champs Affines. We consider the case where T is the theory of C∞-rings: the case of synthetic differential geometry. In particular, we work towards a deffnition of smooth ∞-vector bundles with flat connection. To that end we analyse the tangent category of the category of C∞-rings and Kock's simplicial model for synthetic combinatorial differential forms which may be understood as an ∞-categorification of Grothendieck's de Rham space functor.
dc.description.sponsorshipUtrecht University
dc.format.extent294306 bytes
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.titleStacks and their function algebras.
dc.type.contentMaster Thesis
dc.rights.accessrightsOpen Access
dc.subject.courseuuMathematical Sciences


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