?? various weirdnesses connected with various "tannakian" ideas .... ??? some / all contributing to weirdness of using name "tannakian" for certain things .... ???

?? old (...) idea of "hierarchy of tannaka-krein theorems" ... ?? i thought that it was weird that some items seem to want to appear in more than one place in the hierarchy ... ?? like ... "commutative bi-algebra" ... once in connection with "symmetric monoidal category" (???) but then again in connection with "category with two stable tensor products and lax interchange map between them" (??? ....) ..... ?? then halfway decided that this was connected with ... ?? multiple hierarchies ... (?? ...) ?? module hierarchy and co-module hierarchy, for example .... ??? .... ???? but then also ... ?? maybe different flavors of tannaka-krein theorems, some where you (?? try very hard to ??) get precise equivalence between algebra of certain sort and category of certain sort, but then others where algebra of certain sort gives only some special (?? "affine" ??? .... ??? ...) examples of category of certain sort ..... ???? ...

?? again, funny way certain "tannakian" ideas "fold over" on each other / themselves here ... ??? ....