theHigherGeometer

Consider internal categories and in a finitely complete ambient category , and functors .

…is called an infinitary pretopos.

[This was originally posted on Google+ on 19 June 2013.

Thanks to @jeanas on Mathstodon, here’s a fun pair of problems, the first easy, the second not so much.

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!

[this is an old draft that I just had sitting on my laptop, I’m not sure it’s even finished, and I can’t remember the talk I mention – if someone can find it that would be great!

Just over a year ago, the Busy Beaver Challenge group managed to prove and formally verify that the fifth Busy Beaver number is indeed 47,176,870.

Check out this quote from Euclid But if it is composite, some number measures it.

Following on from last post I want to talk about the appropriate notion of morphism between the objects I defined.

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.

Bundle gerbes are a class of objects that are my bread and butter, but there are many different ways of thinking about them.