Reputation
3,635
Next privilege 5,000 Rep.
Approve tag wiki edits
Badges
12 30
Newest
 Necromancer
Impact
~52k people reached

Feb
5
awarded  Necromancer
Jan
11
comment What does the axiom of replacement mean and why should I believe it?
Thanks to @AsafKaragila for the cross-reference, but it seems to me that Replacement is a sufficiently important and difficult issue that every opportunity to explain it is welcome.
Jan
11
revised What does the axiom of replacement mean and why should I believe it?
better title
Jan
11
comment What does the axiom of replacement mean and why should I believe it?
The Axiom-Scheme of Replacement is an important part of 20th century foundational thinking, but most professional mathematicians have no conception whatever of what it means, when they might be using it or what a terrifyingly powerful hypothesis it is. Whilst the question as asked is very naive, it represents a valuable opportunity for logicians to try to explain what it is about. Certainly we need to keep this open.
Jan
11
reviewed Leave Open What does the axiom of replacement mean and why should I believe it?
Jan
5
comment What does it mean to 'discharge assumptions or premises'?
@DanPiponi's comment is far superior to any of the "answers" on this page.
Dec
29
comment Question about Enriched Categories and Functors
@Todd, OK, I didn't think of that, but in the example that I give the "underlying category" is discrete and so not very interesting.
Dec
29
revised Question about Enriched Categories and Functors
added 116 characters in body
Dec
29
answered Question about Enriched Categories and Functors
Dec
20
awarded  Yearling
Dec
20
comment Is there a category in which finite limits and directed colimits *don't* commute
You need to get out and meet more categories!
Dec
16
reviewed Approve Can the maximal eigenvalue of Toeplitz hermitian be bound by one entry?
Dec
10
comment Distribution of definable integers
Combining the other comments, I would think that your function must be asymptotically larger than any that can be expressed in the particular syntax that you are considering, @JoelDavidHamkins might have some idea of whether or how it can be the "supremum" of such functions. (The quotes are because such functions form a non-Archimedean and therefore Dedekind-incomplete semiring.)
Dec
5
comment History of Mathematical Notation
@PietroMajer, do you have evidence for this? Algebra was developed in Italian, where the word is just "e" and the "t" from Latin had been wasted.
Dec
1
revised In a fibration, where does the generic object live?
added a paragraph of preliminary explanation of the terminology.
Dec
1
comment In a fibration, where does the generic object live?
"$p$ of that object is $\Omega$" is the same as saying that the object is in the fibre over $\Omega$, as you remarked in your comment of 18 November, although I would use $\Omega$ for the fibre containing the generic predicate, not the generic object. I fail to see what you consider wrong with my explanation and how yours is somehow the correct one.
Nov
28
comment Cotensor vs exponential objects.
Are your "many algebraic situations" just abelian categories or do you have experience of cotensors in other settings? I am thinking of the category of algebras for some strong monad over $\mathcal V$.
Nov
24
reviewed Approve Practical advantages of univalent foundations
Nov
23
revised In a fibration, where does the generic object live?
bits of formatting
Nov
23
revised In a fibration, where does the generic object live?
new tag and bits of grammar