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I have split off the section on points-to-pieces transform from cohesive topos and expanded slightly, pointing also to comparison map between algebraic and topological K-theory
I have added to the Examples a section Bundle equivalence and concordance with a quick note on how the points-to-pieces-transform applied to an internal hom of the form $[X,\mathbf{B}G]$ gives the canonical map from $G$-principal bundles with equivalences between them to $G$-principal bundles with concordances between them.
I noticed that at points-to-pieces transform there had been no mentioning of its incarnation in global equivariant homotopy theory; so I went and briefly added a pointer: here
I had some trouble remembering, or making Google remember, where we recorded that “pieces have points” is equivalent to “discrete objects are concrete”.
I have now made a brief remark on that here, where this is more likely to be found (hopefully). I’ll want to turn this into a more comprehensive and polished discussion, but no time right now.
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