?? ... pro-monoidal category ....

?? ... quadratic operad ....

"deformation cohomology" ... reverse-engineering example from ordinary algebraic variety .... ???? .... ???singularity ??? .... ...

?? ... "family of commutative monoid operations" ... ??? ....

action ... ??? ....

?? plenty of quadratic operads that don't come from pro-monoidal categories ... ??? .... ??? other direction ??? ..... ... ?? "something extra" here ??? ... ... ??if it works at all ... ??? .....