# Condensed Objects #

This file defines the category of condensed objects in a category `C`

, following the work
of Clausen-Scholze and Barwick-Haine.

## Implementation Details #

We use the coherent Grothendieck topology on `CompHaus`

, and define condensed objects in `C`

to
be `C`

-valued sheaves, with respect to this Grothendieck topology.

In future work, we will define similar Grothendieck topologies on the category of profinite sets
and extremally disconnected sets, and show that the three categories are equivalent (under
suitable assumptions on `C`

).

Note: Our definition more closely resembles "Pyknotic objects" in the sense of Barwick-Haine, as we do not impose cardinality bounds, and manage universes carefully instead.

## References #

- [barwickhaine2019]:
*Pyknotic objects, I. Basic notions*, 2019. - [scholze2019condensed]:
*Lectures on Condensed Mathematics*, 2019.

`Condensed.{u} C`

is the category of condensed objects in a category `C`

, which are
defined as sheaves on `CompHaus.{u}`

with respect to the coherent Grothendieck topology.