bio  website  PaulTaylor.EU 

location  London & Birmingham, UK  
age  
visits  member for  5 years 
seen  15 hours ago  
stats  profile views  1,822 
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.
21h

comment 
Using the intuition from the arithmetic of cardinal numbers to ascribe values to functions on the extended real line?
In case you haven't heard of them already, you might like to look up the Conway or Surreal Numbers. Is this natural, productive or powerful? I doubt it. 
2d

reviewed  Approve Is there a probability theory developed in intuitionistic logic? 
Dec 15 
revised 
Existence of internal toposes/inner models in a topos
corrected link to my book 
Dec 15 
revised 
Existence of internal toposes/inner models in a topos
added consistency and incompleteness 
Dec 15 
revised 
Existence of internal toposes/inner models in a topos
added link to MO answer on AUs 
Dec 15 
answered  Existence of internal toposes/inner models in a topos 
Dec 14 
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PreOrder induced by continuous functions
I believe that this conjecture is false for reasons of easy real analysis (or order theory). I also consider that the categorical language is obfuscating the problem. (Note that I am a categorist saying this.) 
Dec 14 
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PreOrder induced by continuous functions
I don't follow your notation. If you only have a preorder then it would be better to say glb, inf or meet rather than limit and orderpreserving function rather than functor. Presumably the objects of the preorders are the points of $X$ and you are defining $x\leq_f y$ where $x,y\in X$? The subscripts look confused. What is $R_f$? 
Dec 12 
answered  Can one make a category concrete by “enlarging the universe”? 
Dec 10 
awarded  Synonymizer 
Nov 5 
answered  Math books for advanced high school students 
Nov 2 
revised 
Extensionality in HoTT versus extensionality in internal language of a category
trimmed the suppicatory language 
Nov 2 
revised 
Extensionality in HoTT versus extensionality in internal language of a category
added 250 characters in body 
Nov 2 
comment 
Extensionality in HoTT versus extensionality in internal language of a category
My post was written exactly to be diplomatic, and tutorial, with a view to encouraging the questioner to pursue the study of this topic. Unfortunately, the same cannot be said of most of the responses to naive questions from students that appear on this site: similarly phrased questions on slightly different topics are peremptorily closed. 
Nov 2 
revised 
Extensionality in HoTT versus extensionality in internal language of a category
added 381 characters in body 
Nov 2 
answered  Extensionality in HoTT versus extensionality in internal language of a category 
Oct 27 
reviewed  Approve How to construct a semipositive definite matrix in this form: (L=DA') 
Oct 23 
answered  Disruptive innovations in mathematical notations 
Oct 23 
answered  Are there examples of families of objects which are canonically isomorphic, but where diagrams of canonical isomorphisms don't commute? 
Oct 23 
comment 
Characterize the category of rings
@Tom, doesn't your observation work equally well with any algebraic theory in place of rings? It seems to be defining the thing essentially in terms of itself. 