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Sep 7, 2020 at 17:16 answer added Tim Campion timeline score: 3
Sep 7, 2020 at 17:08 history edited varkor CC BY-SA 4.0
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Sep 7, 2020 at 17:05 comment added varkor @TimCampion: yes, that's right. Compact Hausdorff spaces is another example I would be interested in: I'll update the question, thanks.
Sep 7, 2020 at 16:55 comment added Tim Campion I think you're asking the following: We're given a presentation $(\Omega, E)$, where $\Omega$ is a specification of a class of function symbols for each arity $n \in CARD$ and $E$ is a class of equations in the language $\Omega$. We want to determine whether the category of free algebras $\mathcal T$ for this presentation is varietal, i.e. locally small. Right? One thing to note is that it's equivalent to ask whether the underlying set of each free algebra $T \in \mathcal T$ is small. Another theory one might like to treat would be compact Hausdorff spaces (in terms of ultrafilter convergence)
Sep 6, 2020 at 13:11 history edited varkor CC BY-SA 4.0
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Sep 6, 2020 at 13:03 history asked varkor CC BY-SA 4.0