2,298 reputation
619
bio website PaulTaylor.EU
location London, UK
age
visits member for 4 years, 8 months
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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.

2d
reviewed Approve suggested edit on Is there an example of an SDE that has no weak solution?
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
21
comment Infinite subset of a closed set
False. Let $E=\mathbb R$ and $F=\mathbb N$ inside it.
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).
Aug
17
revised a dcpo seen as a category: when does a dcpo map induce a functor with an adjoint?
added 638 characters in body
Aug
17
answered a dcpo seen as a category: when does a dcpo map induce a functor with an adjoint?
Aug
17
revised Directed subposet of a poset containing the minimal elements
added 255 characters in body
Aug
17
comment Directed subposet of a poset containing the minimal elements
I had in mind that $E$ would get closed under directed joins too. But Werner gave us no idea of where his construction came from and his presentation suggested that is was not definitive but open to experimentation. I tried to make what sense of it I could.
Aug
17
comment What is the status of the extreme value theorem in forms of constructive mathematics, such as Smooth Infinitesimal Analysis?
I do not see where uniform continuity has a bearing on this particular question. I introduced the term occupied compact subspace in my paper as the lattice dual of inhabited overt subspace. Occupation and habitation are not the same thing.
Aug
17
comment Directed subposet of a poset containing the minimal elements
Whoever you are, why have you down-voted me?
Aug
17
reviewed Reject suggested edit on nontrivial theorems with trivial proofs
Aug
17
answered Directed subposet of a poset containing the minimal elements
Aug
17
revised How were formulas / images added to books in post-printing-press / pre-digital times?
added grey and white
Aug
17
revised How were formulas / images added to books in post-printing-press / pre-digital times?
added 163 characters in body
Aug
17
revised How were formulas / images added to books in post-printing-press / pre-digital times?
adopted Carlo Beenakker's version and struck out my own.