Let G be a (not necessarily linear) algebraic group and H a closed algebraic subgroup. Does the, say categorical, quotient G/H exist?  

If yes, where do I find a proof?  

If no, do you have a counterexample?


Remark: I am aware of the following MO discussion, but it does not answer my question: [Quotient of an algebraic group](https://mathoverflow.net/questions/156963/quotient-of-an-algebraic-group-by-a-closed-algebraic-subgroup)



Quotient of a (non-linear) algebraic group by a closed subgroup
See SGA3, Exp. VI$\_{\rm{A}}$, Theorem 3.2(iv): for any group scheme $G$ locally of finite type over a field $k$ and any closed subgroup scheme $H$ there exists a locally finite type $k$-scheme $G/H$ equipped with a faithfully flat $k$-morphism $G\rightarrow G/H$ invariant under the right $H$-action such that $G×H→G\times\_{G/H}G$ is an isomorphism. Thus, this has all "good" quotient properties you could ever want (for maps out, maps in, geometric points, etc.), by descent theory. (The result also holds over any artinian local ring, assuming $H$ is flat.)


