bio  website  PaulTaylor.EU 

location  London & Birmingham, UK  
age  
visits  member for  4 years, 10 months 
seen  10 hours ago  
stats  profile views  1,700 
I am an independent researcher in the foundations of mathematics and computation, using the techniques of category theory and type theory. I wrote a book called Practical Foundations of Mathematics (CUP 1999). My main work now is Abstract Stone Duality, which seeks to axiomatise computable general topology directly, without any recourse to set theory. I am also the author of a TeX package for drawing categorical diagrams.
13h

answered  Is there a standard notation for binary relations in category theory? 
Oct 9 
comment 
Orthogonal FS become weak FS if you switch classes
Please would you say what you mean by strong and weak. I am not sure that I have heard such terminology before for factorisation systems. Besides, these words are grossly overused in mathematics. 
Sep 30 
awarded  Explainer 
Sep 24 
awarded  Autobiographer 
Sep 2 
revised 
Is the fixed point property for posets preserved by products?
precise reference for theorem 
Sep 2 
revised 
Is the fixed point property for posets preserved by products?
added note about accents 
Sep 2 
comment 
Is the fixed point property for posets preserved by products?
(All the other references here are behind a paywall but) the Schroder paper contains some interesting arguments that are similar to ones that have been used in domain theory. Unfortunately, the discussion on this page is an example of the way that pure mathematicians and computer scientists (by which I mean the inhabitants of university buildings so called  we are all mathematicians) talk past one another. I have given a similar theorem and its background from computer science  what it the background for these fixed point results for posets in pure mathematics (departments)? 
Sep 2 
comment 
Is the fixed point property for posets preserved by products?
There are many interesting professional issues behind Joel's comment that I would be delighted to debate with him. Moreover, MathOverflow, as an interdisciplinary site, ought to be the place in which to do so. Unfortunately, its oligarchy has succeeded in preventing any such debate from taking place. 
Sep 2 
comment 
Is the fixed point property for posets preserved by products?
I believe Emil's reference is correct. Maybe he can also tell us whether Bekic's name should have an acute or hachek. 
Sep 2 
revised 
Is the fixed point property for posets preserved by products?
fixed syntax of link 
Sep 2 
revised 
Is the fixed point property for posets preserved by products?
added BekicJones link 
Sep 2 
comment 
Is the fixed point property for posets preserved by products?
As`Andrej said, whether you regard this as an "open" problem depends on whether you're looking for a theorem or a counterexample. In any area of mathematics, a random conjecture expressed in inappropriate generality is likely to be false, with unenlightening counterexamples. This result comes from the practical task of giving mathematical meaning to programming languages. As Francois explains, it requires a cartesian closed category with fixed point operators; domain theory provided many such categories. Yes, I agree that the argument is bizarre. 
Sep 2 
revised 
What structure has been found for functions with this relationship.
added 262 characters in body 
Sep 1 
revised 
What structure has been found for functions with this relationship.
added Pataraia and Bekic 
Sep 1 
revised 
Is the fixed point property for posets preserved by products?
added missing brackets 
Sep 1 
revised 
Is the fixed point property for posets preserved by products?
made "fix" mathsf 
Sep 1 
answered  Is the fixed point property for posets preserved by products? 
Aug 22 
revised 
a dcpo seen as a category: when does a dcpo map induce a functor with an adjoint?
added general Galois connections 
Aug 20 
comment 
Directed subposet of a poset containing the minimal elements
Werner, if you had said that the background to your question was combinatorial group theory, to which you had applied operads and other category theory, then you would have got much more informative answers. If you reduce these things to order theory you probably lose the entire conceptual content. Please edit your question so that I can remove my downvote. 
Aug 20 
comment 
a dcpo seen as a category: when does a dcpo map induce a functor with an adjoint?
Wikipedia is an unquestioned authority? In Galois theory the relationship between subfields and subgroups is contravariant. 