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In 1978, in a series of unpublished conferences in Montréal, A. Joyal announced a remarkable theorem that unified several completeness theorems for fragments of first order logic, as well as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