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18h

comment 
In what sense are fields an algebraic theory?
@DinakarMuthiah, you can try: "the object $F$ is a field iff every morphism out either has codomain equal to the terminal object, or else its a monomorphism." Note that in the category of rings, the "fields" in this sense are precisely the simple rings, so they're more general than division rings. 
Jul 28 
comment 
Does every Lawvere theory arise in this way?
@GiorgioMossa, is that clearer? We require it to be a full subcategory, if that helps. 
Jul 28 
revised 
Does every Lawvere theory arise in this way?
added 64 characters in body 
Jul 28 
comment 
Does every Lawvere theory arise in this way?
@ZhenLin, that's okay; sets are the models of the initial Lawvere theory. 
Jul 28 
revised 
Does every Lawvere theory arise in this way?
added 217 characters in body 
Jul 28 
comment 
Does every Lawvere theory arise in this way?
@ZhenLin, interesting! 
Jul 28 
comment 
Does every Lawvere theory arise in this way?
@DavidRoberts, thank you, yes. I bounce between $\mathbb{F}$ and $\mathbb{K}$ for my fields haha... 
Jul 28 
revised 
Does every Lawvere theory arise in this way?
edited body 
Jul 28 
asked  Does every Lawvere theory arise in this way? 
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 selfenriched. 
Jun 4 
revised 
What are some examples of noncommutative $\mathbb{Q}$monoids and/or $\mathbb{R}$monoids?
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Jun 4 
asked  What are some examples of noncommutative $\mathbb{Q}$monoids and/or $\mathbb{R}$monoids? 
May 16 
comment 
What recent programmes to alter highlyentrenched 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
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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 ordinalindexed sequences? 