Is the category of Coalgebras over a field a topos? I have found several conflicting views about this scouring the litrature. In the least i'm pretty sure that the yonneda embedding for the category of coalgebras has a left exact left adjoint. But then I saw on the nlab that there's a name for this condition: "lex total" and there's also a theorem stated there that the only reason for a lex total category to not be a topos is that the set of isomorphism classes of objects is too big...