reference: Bill Lawvere, [[axiomatic cohesion]], [pdf](http://www.tac.mta.ca/tac/volumes/19/3/19-03.pdf) ## II. Cohesion versus non-cohesion; quality types He interprets geometric morphisms as ``Contrasts'' between cohesion and non-cohesion and between variation and non-variation. There is also a distinction between cohesion and variation. +-- {: .num_defn} ###### Definition A full and faithful functor $f^*: S\to F$ between [[extensive categories]] which is a [[nLab:frobenius functor]] in that it is reflective and coreflective by the same functor by definition *exhibits $F$ as a quality type over $S$. =--