Reputation
Next tag badge:
94/100 score
27/20 answers
Badges
2 60 135
Newest
 Revival
Impact
~403k people reached

Aug
8
answered What is a (-1)-morphism?
Aug
8
revised What is a (-1)-morphism?
edited tags
Aug
6
comment Vector space bases without axiom of choice
Just because we can't describe the basis doesn't mean it doesn't exist! For this particular example, if the axiom of choice holds up to a sufficiently large cardinal, then $F^{\mathbb{N}}$ would have a basis. But the axiom of choice could still fail higher up.
Aug
6
comment Objects with a “Homogeneity Principle”
That looks more like the property of being "Galois"!
Aug
6
comment What are the main differences between set theory versus pure type systems?
The Wikipedia article is short on details. Have you looked at the nLab article?
Aug
5
comment what is expected from a PhD student?
It is also important to know where the gaps in one's knowledge are!
Aug
5
comment Real world applications of category theory
I did not assert that category theory has applications in engineering either. I have not upvoted or downvoted any of the answers in this question as such.
Aug
5
comment Real world applications of category theory
@Did I didn't downvote, but I didn't upvote either: this answer asserts non-existence of applications, which by its nature cannot be backed by evidence.
Aug
4
asked The two-sided simplicial bar construction is Reedy-cofibrant
Aug
4
comment Dependence of Dedekind's Theorem on AC using Scott's trick
Which Dedekind's theorem?
Aug
4
answered Are the hom sets in the category of varieties abelian groups?
Aug
3
comment Confusion about Homotopy Type Theory terminology
That's taking the arithmetic analogy rather too far, I think!
Aug
3
answered Confusion about Homotopy Type Theory terminology
Aug
3
comment Confusion about Homotopy Type Theory terminology
This is standard in dependent type theory, and is rooted in mathematics: after all, what is $X \times Y$ if not the sum of $X$-many copies of $Y$?
Aug
3
comment A Turing machine for which halting is outside ZFC
@ThomasAndrews Whether or not $T$ halts depends on the set-theoretic universe. In a model of $\mathrm{ZFC} + \lnot \mathrm{Con}(\mathrm{ZFC})$, $T$ will halt, and in a model of $\mathrm{ZFC} + \mathrm{Con}(\mathrm{ZFC})$, $T$ will not halt. Since both of these theories are consistent if ZFC is, it must be the case that the halting of $T$ is independent of ZFC.
Aug
3
answered A Turing machine for which halting is outside ZFC
Aug
3
comment Definition of equalizer for $\textbf{Sh}(X)$
Yes, that has the correct universal property. The reason why people don't bother defining it explicitly is because the universal property is enough to pin it down up to isomorphism!
Aug
2
comment The “depth” of a set
This is precisely the concept of set-theoretic rank.
Aug
2
answered Mac Lane exercise - Elegant comma category exercise proven by S.A Huq
Aug
2
comment On consistency of axiomatic systems
I've replaced the definition of completeness with another one. Perhaps this one is more to your liking, but it is equivalent to the one I gave before even for intuitionistic logic.