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Currently, tight acset morphisms don't support limits. But most limits in this category are actually easy: connected limits (notably equalizers) in slice categories are computed as in the underlying category, and products are pullbacks. So we can compute equalizers of tight acset morphisms objectwise over $S_0$ and binary products by pulling back over weights, i.e. $(F\times G)(s:S_0)={(f,g)\in F(s)\times g(s)\mid \forall w : S_\to(s,\top) w(f)=w(g)}.$ (Sorry, curly braces aren't escaping right?)
Terminal objects won't be finite when attribute types aren't, so that's no good, but it seems like it might be nice to have everything else?
The text was updated successfully, but these errors were encountered:
Currently, tight acset morphisms don't support limits. But most limits in this category are actually easy: connected limits (notably equalizers) in slice categories are computed as in the underlying category, and products are pullbacks. So we can compute equalizers of tight acset morphisms objectwise over$S_0$ and binary products by pulling back over weights, i.e. $(F\times G)(s:S_0)={(f,g)\in F(s)\times g(s)\mid \forall w : S_\to(s,\top) w(f)=w(g)}.$ (Sorry, curly braces aren't escaping right?)
Terminal objects won't be finite when attribute types aren't, so that's no good, but it seems like it might be nice to have everything else?
The text was updated successfully, but these errors were encountered: