Given a category $C$, we have its ind-completion $Ind(C)$ whose objects are filtered diagrams in $C$. Assuming the axiom of choice, is any object in $Ind(C)$ isomorphic, in $Ind(C)$, to an ordinal ...
Background for the curious reader: An ordinal $\beta$ is a transitive set in the sense that $\alpha\in\beta$ implies $\alpha\subset\beta$. Any ordinal is naturally well-ordered under $\in$ (so any ...
I wonder if the category $\Delta$ of finite totally ordered sets and monotone functions has binary products and coproducts. In particular, is the ordinal sum a categorical coproduct and/or is there ...