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visits | member for | 2 years, 10 months |
seen | 2 days ago | |
stats | profile views | 469 |
Jun 27 |
comment |
What is the general opinion on the Generalized Continuum Hypothesis?
The problem with this viewpoint in my opinion, Tom, is that a topos is meant to have sets for homsets, and those sets are meant to live in a universe of sets, and that universe either satisfies $\mathrm{GCH}$, or it doesn't. But perhaps this can be gotten around somewhat by considering each topos as canonically self-enriched. |
Jun 4 |
revised |
What are some examples of non-commutative $\mathbb{Q}$-monoids and/or $\mathbb{R}$-monoids?
added 71 characters in body |
Jun 4 |
asked | What are some examples of non-commutative $\mathbb{Q}$-monoids and/or $\mathbb{R}$-monoids? |
May 16 |
comment |
What recent programmes to alter highly-entrenched mathematical terminology have succeeded, and under what conditions do they tend to succeed or fail?
@KConradk, or calling covariant functors "functors" and contravariant functors "cofunctors." |
May 14 |
comment |
What questions should -ologists of mathematics ask, in order to improve maths researcher training?
Is undergraduate mathematics considered part of "mathematics researcher training"? |
May 14 |
awarded | Civic Duty |
Apr 13 |
revised |
Category theory and model theory as “natural” counterparts
added 1040 characters in body |
Apr 13 |
answered | Category theory and model theory as “natural” counterparts |
Apr 5 |
revised |
Is there a “large powerset axiom” so extreme that it disproves the existence of strongly inaccessible cardinals?
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Apr 5 |
comment |
Is there a “large powerset axiom” so extreme that it disproves the existence of strongly inaccessible cardinals?
@ToddTrimble, yep, I find your argument utterly persuasive. Its worth pointing out that "beg the question" is no shorter than "assume the conclusion," and much more ambiguous. In any event, the statement I was nearly persuaded by, namely: "it cannot be denied that logic and philosophy stand to lose an important conceptual label should the meaning of [beg the question] become diluted" is clearly false in light of your comment. |
Mar 23 |
accepted | Good set theory in which to study ordinal-indexed sequences? |
Feb 25 |
awarded | Nice Question |
Feb 23 |
comment |
The groupoid of algebraic expressions and proofs
@SylvainJULIEN, that's an intense look question fella. What, in particular, do you think the connection might be? By the way, your previous comment made my day. :) |
Feb 20 |
comment |
The groupoid of algebraic expressions and proofs
@AndrejBauer, well the path category of a quiver is associative precisely because the domain of the forgetful functor $\mathbf{Cat} \rightarrow \mathbf{Quiv}$ is $\mathbf{Cat}$. It should be the same thing here; by choosing an appropriate forgetful functor, with the correct domain, its left adjoint should build an associative structure "automatically". |
Feb 16 |
comment |
How have mathematicians been raised?
Step 0. Don't force them to do math. Ever. Step 1. Tell them interesting puzzles at their current level of development. Step 2. Set up somewhere to lie outside, so they can gaze up at the heavens, and wonder. To quote Atiyah: "In the broad light of day mathematicians check their equations and their proofs, leaving no stone unturned in their search for rigour. But, at night, under the full moon, they dream, they float among the stars and wonder at the miracle of the heavens. They are inspired. Without dreams there is no art, no mathematics, no life." Step 4. Don't force them to do math. Ever. |
Feb 15 |
comment |
The groupoid of algebraic expressions and proofs
@PaulTaylor, now if you can see a way of describe the construction of interest by abstracting the concept "Lawvere theory" and considering "Lawvere theory objects in a $2$-category $\mathbf{C}$ with sufficient structure", and then choosing $\mathbf{C}$ carefully to explain the construction of interest, well this would be very interesting. I cannot currently see how to do this, however, and your answer offers absolutely no hints or suggestions in this direction. |
Feb 15 |
comment |
The groupoid of algebraic expressions and proofs
@PaulTaylor, you misunderstand me. I would very much like to be able to view this as a special case of a more fundamental construction, perhaps the left-adjoint to some $2$-functor or some such. Nonetheless, the point remains that this groupoid-like-object is not a Lawvere theory in the usual sense of the word, and it cannot be recovered from the Lawvere theory. The act of passing from the presentation to the Lawvere theory throws away too much information, and we can't recover the groupoid of interest. |
Feb 13 |
comment |
The groupoid of algebraic expressions and proofs
Interesting. There's definitely a strong connection there. |
Feb 13 |
comment |
The groupoid of algebraic expressions and proofs
@TheMaskedAvenger, do you mean absolutely free algebra? |
Feb 13 |
accepted | Has this construction, which builds a symmetric multicategory from a commutative monoid, been described or studied anywhere, and if so, where? |