Category Theory
Zulip Server
Archive

You're reading the public-facing archive of the Category Theory Zulip server.
To join the server you need an invite. Anybody can get an invite by contacting Matteo Capucci at name dot surname at gmail dot com.
For all things related to this archive refer to the same person.

Stream: deprecated: topos theory

Topic: Inverse limits of toposes

Jens Hemelaer (Aug 27 2020 at 14:20):

Certain Galois toposes can be written as $\lim_{i \in I} \mathbf{PSh}(G_i)$ where $(G_i)_{i \in I}$ is an inverse system of discrete groups. (The limit is a strict limit in the 2-category of toposes and geometric morphisms.)

Does anyone here know what the objects and the morphisms in this topos are?

If all groups $G_i$ in the diagram are finite, then I believe the objects of the topos are sets $S$ together with a $G$-action, with the special property that the action morphism $G \to \mathrm{End}(S)$ factors through one of the groups $G_i$. The morphisms are the functions such that $\phi(g\cdot x) = g\cdot \phi(x)$ for all $g\in G$. Can you do the same in general?

Jens Hemelaer (Aug 28 2020 at 15:43):

I asked the same question on mathoverflow: https://mathoverflow.net/q/370330/37368
(The question is answered! Also, there is a mistake in my description above, see the comments to the question.)