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16 votes
1 answer
3k views

Forcing in Homotopy Type Theory

I apologize if this question doesn't make any sense. I'll just go ahead and delete it if that's the case. But the question is just the title. Is there a notion of forcing in homotopy type theory? Pr …
Jonathan Beardsley's user avatar
7 votes
1 answer
522 views

Which morphisms of ring spectra are of effective descent for modules?

There is a well understood bifibration of $\infty$-categories over the $\infty$-category of commutative ring spectra whose fiber over a ring $R$ is the category of $R$-module spectra. This is in analo …
Jonathan Beardsley's user avatar
5 votes
1 answer
660 views

Associative Ring Spectra and Derived Completion

So, I was thinking before that this might have some nice, simple topos theoretic explanation, but Jacob disabused me of that notion. However, I'm still very interested in the following question: Is …
Jonathan Beardsley's user avatar
4 votes
1 answer
152 views

Are monomorphisms in an $\infty$-topos preserved by $0$-truncation?

Let $\mathfrak{X}$ be an $\infty$-topos and let $f\colon X\to Y$ be a morphism of $\mathfrak{X}$. We say that $f$ is a monomorphism if it is $(-1)$-truncated which means that for every $Z\in\mathfrak{ …
Jonathan Beardsley's user avatar