Full Idea
There is a dedicated contingent who hold that the category of 'categories' is the proper foundation for mathematics.
Gist of Idea
Categories are the best foundation for mathematics
Source
Stewart Shapiro (Thinking About Mathematics [2000], 10.3 n7)
Book Reference
Shapiro,Stewart: 'Thinking About Mathematics' [OUP 2000], p.272
A Reaction
He cites Lawvere (1966) and McLarty (1993), the latter presenting the view as a form of structuralism. I would say that the concept of a category will need further explication, and probably reduce to either sets or relations or properties.