???"hartog" fan / theory (...) of (?? nice?? ...) commutative monoid .... ???? .... ?? especially non-invertible morphisms in theory ?? ... ???? ....

?? ... kummer ...???? ....

?? strictification (of theory ... ?? ...) here ??? ....

??relationship between stuff about "TAG toposes" we've been studying semi-recently, and ... ??? stuff todd's mentioned about .... ???? "faithful representation of theory of symmetric monoidal closed categories ..." ?? .... ????