it is rumoured that zariski was rather annoyed with grothendieck, since prior to the latter's introduction of sheaves and cohomology into algebraic geometry, only zariski could do the subject whereas subsequntly any idiot could. equally, much of grothendieck's enterprise is purely categorical so we could reasonably expect similar results in, for example, dynamical systems. an example in the litterature that was crying out for such an interpretation was adam epstein's various generalisations of thurston's rigidity of post critically finite rational maps, which we'll put, and improve, in their natural context of a dynamical topus. en passant this also leads to some highly clarifying results about real blow ups.