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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeJun 9th 2022
   • (edited Jun 9th 2022)
   • PermaLink
   Author: Urs
   Format: MarkdownItexGiven the recent edits, allow me to ask: * Has anyone looked into formalizing [[topological K-theory]] in homotopy type theory? We are specifically after [[twisted equivariant K-theory]], for which it would be important to have not any construction of [[KU]], but to have specifically the space of *[[Fredholm operators]]* axiomatized as a topological (real-cohesive) 0-type, whose [[shape modality|shape]] would give $KU$. Does this seem feasible, to formalized spaces of [[Fredholm operators]] in (real-)cohesive homotopy type theory, and proceed from there to a discussion of topological K-theory? Has anything in the direction been looked at before (separable Hilbert spaces, bounded linear operators, ... in HoTT)?

   Given the recent edits, allow me to ask:

   • Has anyone looked into formalizing topological K-theory in homotopy type theory?

   We are specifically after twisted equivariant K-theory, for which it would be important to have not any construction of KU, but to have specifically the space of Fredholm operators axiomatized as a topological (real-cohesive) 0-type, whose shape would give $KU$.

   Does this seem feasible, to formalized spaces of Fredholm operators in (real-)cohesive homotopy type theory, and proceed from there to a discussion of topological K-theory? Has anything in the direction been looked at before (separable Hilbert spaces, bounded linear operators, … in HoTT)?