??factorization system involving cohesive (or something) geometric morphism??...

???something about "sequent" vs "sentence" and so forth... ??confusion about factorization systems here... ??and so forth... ???something about whether sequents give formulas in _intuitionistic_ (or something...) logic... ???something about interaction between "conjunction" at different "levels"...

exploitation of cryptomorphism... secondary operation ... ??horn logic ... ??asf??? ... ??something about sketches vs formulas... "multidimensional algebra" .. ???...

"diaconescu's theorem" for various doctrines... ???...

zombie chesire cat... pincushion...

??something about serre ideal subcategories and so forth... ??... ??"viable sub-lizard" and so forth...