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diff --git a/content/zettel/4d1.md b/content/zettel/4d1.md new file mode 100644 index 0000000..564ccd2 --- /dev/null +++ b/content/zettel/4d1.md @@ -0,0 +1,22 @@ ++++ +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 |