[Alta-Logic] Stacks Seminar

[Ben MacAdam]

Hi everyone,

The stacks seminar will resume next week:

Speaker: Jonathan Gallagher

Time and Location: 12:00 Friday, October 26 in ICT 616

Title: Locally presentable categories, smooth sheaves, and smooth stacks

Abstract:
Locally finitely presentable categories provide a theoretical tool
that we will reuse in various ways throughout this seminar series.

First, they generalize categories of sheaves, as reflective subcategories 
of presheaf categories, but where the left adjoint need not be finitely
continuous.  These still carry a certain amount of "local" data with them,
and can be useful for geometry in their own right.

Second, they are categories of models of essentially algebraic theories.
For example, Cat is locally presentable as it is the category of models 
of the theory of categories.  

We can then combine these two views, and talk about categories enriched 
in a locally presentable, monoidal closed category.  In this case, we can 
take enriched presheaves into the base, and talk about enriched locally presentable
categories and enriched categories of sheaves.  If we do this for Cat-enrichment,
we get stacks.

In future seminars, we will build upon this viewpoint to additionally talk about
smooth sheaves and smooth stacks in a way inspired by SDG and smooth toposes.