Categorytheory on Patrick Stevens

Representable functors

Tue, 26 Jan 2016 00:00:00 +0000

Just a post to draw attention to my new article about representable functors and their links to adjoint functors. It’s very short, but it gives a reason for being interested in representable functors: they are basically “those with left adjoints”, up to minor quibbles.

Monadicity Theorems

Thu, 31 Dec 2015 00:00:00 +0000

Another short post to highlight the existence of an article about the Monadicity Theorems, in which I prove one direction of both the Crude and Precise versions. Comments and corrections would be very much appreciated, because there is an awful lot of work involved in proving those theorems. It would be good to know of any parts where the argument is unclear, unmotivated, too long-winded, or wrong.

General Adjoint Functor Theorem

Thu, 24 Dec 2015 00:00:00 +0000

Just a post to draw attention to my new article about the General Adjoint Functor Theorem. It’s a motivation of the GAFT and its proof. I’ve never seen it motivated in this way, and it’s actually quite a natural theorem. I haven’t managed to motivate the Special Adjoint Functor Theorem at all, although I’m told that it’s natural if you know Stone-Cech compactification.