2
votes
0answers
111 views

Hosting Category Theory in a “universe” that is non-LFP

WHen I did my MSc, I was trained by a very talented topologist. I had a passion for the subject before and since. Now I am interested in category theory, but I seem to be very interested in the ...
4
votes
2answers
299 views

Functor category's objects fail to be a class?

Given two categories, we can form the functor category whose objects are functors. Functors by definition consist of two mappings from in general classes to classes, which makes it fail to be a set. ...
14
votes
1answer
520 views

On Joyal's completeness theorem for first order logic

In 1978, in a series of unpublished conferences in Montréal, A. Joyal announced a remarkable theorem that unified several completeness theorems for fragments of first order logic, as well as first ...
8
votes
3answers
937 views

Is there a categorical proof of Gödel's incompleteness theorem?

A significant result in set theory was shown by Cohen when he showed that the continuum hypothesis was independent of ZFC using a new technique called forcing. In Topos theory, this result has a new ...
7
votes
1answer
554 views

Untyped Higher Category Theory

I am currently trying to wade through the vast lake of higher category theory, a formidable task,or so it seems. In the process, it has occurred to me that there is a basic analogy in place with ...
2
votes
2answers
660 views

products in a category without reference to objects or sources and targets

Hi, I was thinking about presenting categories with nothing but equations over morphisms. I wondered about products. The definition of a product has its genesis in the following diagram shape A->B ...
3
votes
1answer
370 views

linear logic, diagrammatic calculus and foundations

Hi, I have been interested in foundations for a while, especially categories as foundations. I am of the opinion that, as long as we present the theory of categories in SET, we will not be able to ...
1
vote
1answer
252 views

continuous maps between categories that are not functors

Hey, Is it possible to define a map between two categories which preserves all products and binary equalizers and yet is not a functor, ie it does not satisfy one or more axioms of a functor? ...