Recently, Bart Jacob’s asked me a question about containers: He is looking for a formula for the derivative of a quotient container. I sketched a possible answer (I haven’t yet checked the details) and used this opportunity to give a quick introduction to containers.
A container is given by a set of shapes and a family of position, giving rise to a functor
given by . It’s derivative as a functor is
. A quotient container is specified by additionally
giving a family of subgroups of the isomorphism group, it gives rise to a functor
where the equivalence relation is generated by for
. I believe that it’s derivative is given by extending the previous formula by additionally specifying
where iff is given by restricting an isomorphim with the property (by restricting I mean that ).