Modal algebra

Stream: maths

[Yaël Dillies]

As part of my order/category series, I'm considering formalizing modal algebras and interior (aka S4) algebras, just so that people know.

[Kevin Buzzard]

Why don't you do things which regular mathematicians have heard of instead of arbitrary low-level objects which nobody will ever use?

[Kevin Buzzard]

You are so insanely productive and helpful, I want to drive you in the right direction :-)

[Kevin Buzzard]

If you want to do something spectacular, prove that a topological space is spectral iff it's isomorphic to Spec of a ring. If you want to do something more mundane but still helpful then there's chapter 3 of https://arxiv.org/abs/1910.05934 (skipping this part); all of this stuff about spectral spaces is important in other areas.

[Yaël Dillies]

My original goal is actually to prove that a topological space is spectral iff it's isomorphic to the spectrum of a lattice, which is closely related. I thought I would immerse myself in this area of maths by defining related stuff as I read about it and, well, I read about modal algebras :^)

[Yaël Dillies]

I understand I am very new to all this math, so I can't judge what's important. If you tell me to work on spectral spaces, I will work on spectral spaces.

[Yaël Dillies]

(but I'll probably keep doing sporadically one-day write ups about random bits of maths because it's just too fun!)