+++
title = "Solutions to Set of all {Sets, Groups, Top. Spaces} does not exist"
author = "Yann Herklotz"
tags = []
categories = []
backlinks = ["4d"]
forwardlinks = ["4b", "4d2"]
zettelid = "4d1"
+++

The problem in Set Theory ([\#4b]) and the other spaces and collections,
is that one cannot build a collection of all collections. In Category
Theory, one has the same problem, not being able to have a Category of
all Categories. There are various possible solutions to this:

-   Bound the size of objects by cardinal κ.
-   Use Classes (from Set Theory: Sets that satisfy first order
    formula).
-   Grothendiek Universes (similar to bounding the size).
-   Ignore the problem (possible for simple category theory).

  [\#4b]: /zettel/4b