daniel gratzer

phd student @ aarhus university. (modal) type theory, (higher) category theory.
he/him. 🏳️‍🌈.

[daniel gratzer @dannygratzer]

@sclv Ah, but it is a dextrification process (making things into right adjoints). The co- here is a reference to cofree: the process is a right adjoint rather than a left adjoint.

(I had the same question :) )

[Computer Science at Aarhus University @csaudk]

What is the next step in your career? Come join the department as a PhD student. The next application deadline is August 1. @BirkedalLars and Peyman Afshani have open positions! But you can also use the general call ➡ https://t.co/f2GS39sEdZ

[daniel gratzer @dannygratzer]

(and indeed, together with some results on 1-cofinality, it is literally a generalization)

[daniel gratzer @dannygratzer]

Huh, so today it clicked for me that the Bousfield-Kan formula for colimits should be understood as the higher-categorical generalization of the classical construction building a colimit out of a (reflexive) coequalizer & coproducts.

[Taichi Uemura @t_uemura669101]

published
https://t.co/mXA3Hqo234

[daniel gratzer @dannygratzer]

What makes this interesting: it's _provably_ impossible in a constructive setting. Having unital completion without the assumption of decidable support for core implies a weak form of the law of excluded middle.

[daniel gratzer @dannygratzer]

While writing this "synthetic Iris" stuff, one thing I found remarkable: Iris uses Cameras for a sort of 'step-indexed partial commutative monoid'. The definition has a lot of random warts though around how partiality is handled. Some of this is pragmatic

[daniel gratzer @dannygratzer]

Turns out, this is a bad idea! You can do everything you expect _except_ give a unital completion of a camera. This would be fine, except the main construction one does with cameras generalizes unital completion.

[daniel gratzer @dannygratzer]

Thesis update: drafts for all chapters except preliminary materials and the conclusion exist! Modulo a few random subsections, things are in good shape.

Two months left to polish & fill in the remaining text.

[daniel gratzer @dannygratzer]

@plain_simon @myers_jaz @taz_chu @mattecapu (Though I am sympathetic to trying to somehow politely phrase the question "why do this thing when it is so much easier to just not do things?")

[daniel gratzer @dannygratzer]

@plain_simon @myers_jaz @taz_chu @mattecapu My usual issue with this question is that "can" in the sense of "is possible" is always true (we can always 'eliminate the cut'). But the useful version of "can" ("would we have done X practically without Y") is sort of an impossible hypothetical.

[daniel gratzer @dannygratzer]

"Cubical type theory can't hurt you"
Meanwhile, cubical type theory:

[daniel gratzer @dannygratzer]

@lambdabetaeta @carloangiuli No, now you're supposed to say "Did you violate that substitution lemma?"

[daniel gratzer @dannygratzer]

Creating some new copy-pasta with @carloangiuli

[daniel gratzer @dannygratzer]

@Karlomancer @carloangiuli PhD students would rather alter the speech from A Few Good Men then write their thesis, etc.

[daniel gratzer @dannygratzer]

@killerswan It didn't get to a date, but I forever think of the tinder guy who tried to convince me that he was part of a startup for Business Sheaf Theory (I mentioned that I was reading a book with Sheaf Theory in the title)

[daniel gratzer @dannygratzer]

The face of a dog witnessing a horrible crime (me eating a carrot and not sharing)

[daniel gratzer @dannygratzer]

@ProfMaxNew @jonmsterling Nice! I have a fairly direct and minimal first thing for the purposes of this thesis, but I'd love to discuss how one might turn it into something more than a pedagogical device/what improvements it might suggest!

[daniel gratzer @dannygratzer]

Currently drafting an explanation of how to build up Iris -internally- to a modal type theory. Essentially hoping this might produce the definition of Iris @jonmsterling has long asked me for *or* an entry point to modal type theory the Iris folks here at AU have also discussed.

[daniel gratzer @dannygratzer]

@tangled_zans @jonmsterling Perhaps this will help with that, though I think I'd require more familiarity with granule to write such a thing more directly I'm afraid