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10 votes
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Examples of differential cohomology in cohesive $\infty$ topos

If we consider just shape modality "$\Pi$" (or "ʃ") and flat modality $\flat$ (which are sufficient for the differential cohomology hexagon, then the traditional arithmetic fracture squares are the le …
Urs Schreiber's user avatar
19 votes
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Learning higher differential geometry

You seem to be asking about my $n$Lab entries on higher differential geometry and related. I have now added there a commented References section with some pointers. See there for an extended and …
Urs Schreiber's user avatar
14 votes
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$\infty$-categorical interpretation of type theory

Mike Shulman has a good discussion of what exactly needs to be shown in his Michael Shulman, "The univalence axiom for inverse diagrams" (arXiv:1203.3253) The issue is that in the type theory the …
Urs Schreiber's user avatar
25 votes
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Forcing in Homotopy Type Theory

In as far as we regard forcing as forming internal sheaves, the question is asking how to say "internal category of sheaves" in homotopy type theory. It is expected that this works in directed analo …
Urs Schreiber's user avatar