Symmetric monoidal closed objects

I conjecture that there’s a compact closed bicategory Th(SMCC) such that the 2-category hom(Th(SMCC), Prof) of

• sylleptic monoidal functors (of bicategories),
• braided monoidal transformations and
• monoidal modifications

is equivalent as a 2-category to the 2-category SMCC of

• symmetric monoidal closed categories,
• braided monoidal closed functors, and
• monoidal closed natural isomorphisms.

If we model Th(SMCC) in the compact closed bicategory 3Cob₂, then we get

where I didn’t draw

• the right unitor
• the pentagon equation for the associator
• the triangle equations for the unitors
• the hexagon equations for the braiding
• the yanking for internal hom
• a,b,c,l,r composed with their formal inverses equals the identity

but I think they’re pretty obvious given this other stuff.