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Michal R. Przybylek's user avatar
Michal R. Przybylek's user avatar
Michal R. Przybylek's user avatar
Michal R. Przybylek
  • Member for 13 years, 9 months
  • Last seen more than 2 years ago
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 Yearling
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 Popular Question
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 Popular Question
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 Enlightened
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 Yearling
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 Enlightened
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Given $A \hookrightarrow X$ and $B \hookrightarrow X$ with trivial intersection, when is $A \sqcup B \to X$ also a monomorphism?
Your key-word here is: ``effective unions''. Check, for example, "ON CATEGORIES WITH EFFECTIVE UNIONS" by Michael Barr.
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Is $2^\mathfrak{m}<2^\mathfrak{n}\Rightarrow\mathfrak{m}<\mathfrak{n}$ equivalent to the axiom of choice?
@Asaf, thanks, I've got it now :-)
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Is $2^\mathfrak{m}<2^\mathfrak{n}\Rightarrow\mathfrak{m}<\mathfrak{n}$ equivalent to the axiom of choice?
@Asaf: thank you! But I think I am still missing something - why can't you use: $(2^A)^A=2^{A^2}=2^A= (2^A)^1$ to infer $A \approx 1$, i.e.~that $A$ is a singleton?
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Is $2^\mathfrak{m}<2^\mathfrak{n}\Rightarrow\mathfrak{m}<\mathfrak{n}$ equivalent to the axiom of choice?
@GuozhenShen: what is the proof of the statement from the paper?
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If a vector space has a basis then its dual vector space has a basis
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If a vector space has a basis then its dual vector space has a basis
thank you (+1) --- this looks very interesting to me, but I need a few moments to dig through the details.
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When are enriched categories equivalent?
@AlexMine, what you have said is simply not true --- you are missing two obvious constant functors.
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