What's the most important part of a space: the points, or the neighbourhoods of points? If you're sober, maybe it doesn't matter.
Category: Co-learning
Whatever the dual notion to “learning” is, that is what I hope to do with the material. In some (most?) cases, this notion may very well be self-dual.
How have I gone this long without talking about monads?
Did you know that reading is a monad? It's because reading is free, and free things are generally monads. What does this even mean? Well, you won't find out by reading this blog, that's for sure...
I don’t know what a stack is…
No, I'm not talking about the data structure.
Every fibre of Galois is fundamentally better than me
Am I writing about Galois again? The title might seem to suggest so, but I just didn't want to title another blog after Grothendieck.
Weekly local blog presents: weakly local presentability
Okay I know my blog isn't anywhere near weekly. Could we stop splitting hairs and just agree that it's weakly weekly?
Control your nerves to keep a good image
Nerves are great when they realise a category as a subcategory of presheaves, but they're even better when we know exactly which presheaves are nerves.
The nerve to be so dense
Nerves are arguably a generalisation of the Yoneda embedding. From this point of view, what would be a generalisation of the Yoneda Lemma for nerves?
Are you blind if you don’t have site?
A Grothendieck topos is a category of sheaves, but what happens if you forget the site over which the sheaves are defined?
Local blog presents: local presentability
Locally presentable categories are very nice, convenient places to work in, so here's a brief summary of some of the ways to recognise when you're in this lucky situation.
Grothendieck this, Grothendieck that
Induce a Grothendieck topology on a Grothendieck construction to prove that Grothendieck topoi are closed under slicing.