>>11111796Here is my main gripe with category theory: this book
> Category Theory for the Working Mathematicianshould be more of an ad for model theory than it is
in fact, there should be some correspondence between logic and category theory since category theory is just meta-mathematics
the book is fundamentally naive, and that is what makes it so infuriating
it should have been sophisticated and beatific, but instead it was slow and disabled
the reason for this, I think, is this obsession with diagrams as if that somehow were sufficient argument to dispense with questions of meta-mathematical rigor
furthermore, category theory injects pure arrogance into mathematics with insistence that objects that exist are
> smallin the sense of small cateogries
whereas objects that don't exist are either regular sized or large, depending on your point of view
the problem here is simply adding a new non-standard name for a concept that already has two names:
- condition
- class
and instead of introducing the necessary meta-mathematical equipment and saying
- a (large) category is defined to be an n-tuple of conditions of the following form
where the n-tuple is
- condition: is this an object in the category
- condition: is this a morphism in the category
- ...
we are just supposed to assume that all of that meta-mathematics and logic is trivial
the level of rigor simply isn't up to that of the rest of mathematics
not only rigor, but finding a fit with existing fields of mathematics and meta-mathematics
