PSA: a category satisfying all but the smallness condition from Giraud’s theorem…
I'm surprised people in the area of condensed mathematics haven't adopted this term that's at least 50 years old
theHigherGeometer
Latest posts
An example of a presheaf without an associated sheaf – UPDATED
On a large site there are presheaves that may not have associated sheaves. I walk through an example of this that is less tied to a specific choice of set theory
A game strategy that depends on the Continuum Hypothesis?
A fun problem about an optimal strategy for a game with ordinals
The ATLAS of Finite Groups is sound
I missed this at the end of last year, but I had been periodically looking to see if it had been done: the last gap in verifying that the ATLAS of Finite Groups is bug-free has been filled! (Added: not formally verified, I might add, just in the old-fashioned sense of the tables being replicated … Continue reading The ATLAS of Finite Groups is sound
Glue work instead of pasting diagrams
Reflections on "glue work"
BB(5)=47,176,870: BB(6) is … astronomically larger
Good news everyone! Even *longer* running halting Turing machines with just six states.
Infinite descent in ancient times
Is this the oldest example of the well-foundedness of the naturals being explicitly mentioned?
Morphisms between abelian differentiable gerbes
Following on from last post I want to talk about the appropriate notion of morphism between the objects I defined. Recall that these are Lie groupoids with a map to the manifold satisfying some properties ( and are surjective submersions), and then equipped with a little bit of extra structure. We will fix a bundle … Continue reading Morphisms between abelian differentiable gerbes
Small fun observation about finite topological spaces, and some challenges
Here’s a fun thing: if you want to generate a random finite space, instead select a random subset from , the -fold power of the Sierpinski space , since every space embeds into some (arbitrary) product of copies of the Sierpinski space. (Recall that has underlying set , and the only open subsets are . … Continue reading Small fun observation about finite topological spaces, and some challenges
Abelian differentiable gerbes – recap
Bundle gerbes are a class of objects that are my bread and butter, but there are many different ways of thinking about them. In my paper with Raymond Vozzo we wrote a different take that starts from the point of view of plain Lie groupoids (which we allow to be infinite-dimensional) and slowly builds in … Continue reading Abelian differentiable gerbes – recap