2,418 reputation
619
bio website PaulTaylor.EU
location London, UK
age
visits member for 4 years, 9 months
seen Sep 11 at 20:37
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.

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 Bekic-Jones 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 down-vote.
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.
Aug
17
revised How short can we state the Axiom of Choice?
edited tags
Aug
17
answered How short can we state the Axiom of Choice?
Aug
17
comment What is the status of the extreme value theorem in forms of constructive mathematics, such as Smooth Infinitesimal Analysis?
I did talk about the attainment of the maximum as well as the maximal value.
Aug
17
comment a dcpo seen as a category: when does a dcpo map induce a functor with an adjoint?
I would say that a Galois connection is a contravariant adjunction $A\to B^{op}$. There are also co-Galois connections, but after a glass of wine or two this evening I am not going to commit myself to saying which is which (see my book).