2,813 reputation
622
bio website PaulTaylor.EU
location London & Birmingham, UK
age
visits member for 5 years
seen 15 hours ago

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
comment Pre-Order 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
comment Pre-Order 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 order-preserving 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 semi-positive definite matrix in this form: (L=D-A')
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.