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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 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?
added 2 characters in body
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?