11,224 reputation
43491
bio website ncatlab.org/nlab/show/…
location Adelaide, Australia
age 31
visits member for 5 years, 4 months
seen 9 mins ago

Pure mathematician interested in category theory and foundations.


19h
comment NCG with all noncommutativity in a nilpotent ideal
Cross posted from MSE math.stackexchange.com/questions/1214990/…
1d
comment Classifying spaces of topological groups whose underlying spaces are homotopy equivalent
@DanRamras The conditions do imply they are good simplicial spaces.
1d
comment “Epicycles” (Ptolemy style) in math theory?
@HaukeReddmann, thanks - perhaps 'mathematical theory'? or 'a math theory'? It looks like a mass noun to my eyes (off topic, sorry for the obsessive nitpicking...)
1d
comment When is the category of small (pre)sheaves a(n elementary) topos?
@TimCampion in the case of Easton forcing, the large category on which you take small (pre)sheaves is the sequential colimit of an ORD-sequence of small posets with the double negation topology, where the functors are the right adjoint part of a fibration of sites a la Moerdijk. Any monomorphism lives in a subcategory that is a topos over some site in the sequence, and so is classified by the subobject classifier in that topos, which is the constant sheaf on 2. That constant sheaf is thus a subobject classifier, but failure of local smallness means no power objects, thus not a topos.
2d
comment “Epicycles” (Ptolemy style) in math theory?
@RobertIsrael cf Maxwell's equations, (A)-(H), starting page 22 of upload.wikimedia.org/wikipedia/commons/1/19/…. Now we can write these as two equations, using differential forms on Minkowski space.
2d
comment “Epicycles” (Ptolemy style) in math theory?
Regarding $\alpha$ as some "symbol" - isn't that what $\sqrt{-1}$ basically was for a long time? The construction $\mathbb{C} := \mathbb{R}[x]/(x^2+1)$ was presumably post-Galois, too.
2d
comment “Epicycles” (Ptolemy style) in math theory?
What is 'math theory'?
2d
comment When is the category of small (pre)sheaves a(n elementary) topos?
I keep urging Daniel Schäppi to write up what he knows about small sheaves and the fpqc site, which is not well-known, or possibly only known to experts of a certain ilk.
2d
comment When is the category of small (pre)sheaves a(n elementary) topos?
It is possible to have a subobject classifier without being a topos. This is what seems to be happening when I think about class forcing via small sheaves. For example the Easton product gives a non-locally small infinitary pretopos with subobject classifier, but since it is not locally small the catesian closed <=> power objects construction doesn't work.
2d
awarded  Nice Question
Mar
30
revised What sort of W-types follow from existence of an NNO?
Typo in expression for F
Mar
30
accepted What sort of W-types follow from existence of an NNO?
Mar
29
comment Are numbers fundamental mathematical entities?
...whether numbers are fundamental entities, whatever that means, so perhaps the title was not chosen well. Douglas' comment is a good one, namely that not all cultures (since this is a HO question) take number as primary, and concepts of counting are notoriously varied across the world.
Mar
29
comment Are numbers fundamental mathematical entities?
Regarding the edit, and Zev's comment, from a structural point of view, any initial object in the category of commutative unital rings is good enough to 'be the integers'. Just like the answer to the question "what is a real number?" is "an element of a complete ordered field", the concept that there is a unique "number 1" is not as pinned down in all foundations. In a topos setting, the number 1 is "the" morphism $\ast \to N \stackrel{s}{\to} N$, given any initial object $\ast$ and any natural number object $N$, neither of which are unique. This line of reasoning seems different to ...
Mar
29
comment Interplay between Loop Quantum Gravity and Mathematics
Interesting higher category theory in the early-mid 90s was somewhat inspired by LQG or precursors, eg work by John Baez.
Mar
29
comment Are numbers fundamental mathematical entities?
As Finnur Larusson, who gave a public lecture recently, said: numbers are something inside peoples' heads, abstracting features of reality. Certainly numbers are among the first, if not the first, abstract mathematical object people wrote down. Periodicity phenomena were probably not long later, but such symmetries were counted with numbers. I think this is a sensible philosophy of mathematics question, if people can give answers citing historical and philosophical research then it shouldn't be closed, IMHO (it has one close vote already).
Mar
28
comment Problems concerning meromorphic 1 form on Riemann surface
I'm voting to close this question as off-topic because it seems to be homework
Mar
26
awarded  Announcer
Mar
26
comment Closed Form Solutions To Simple Iterated Polynomial Building Blocks
You can flag this for moderator attention and ask them to migrate it if you like.
Mar
26
comment Proof : Limit of a sequence
Please do your own homework.