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{\bf On two tricks to make Category Theory fit in less mental space:
  missing diagrams and skeletons of proofs}


When I started studying Category Theory two things in the texts gave
me the impression that CT was incredibly powerful: one was the
suggestion, implicit in the use of the definite article ``the'' in
expressions like ``{\sl the} functor that takes each object $B$ to $A
{\times} B$'', that once we define how a functor acts on objects its
action on morphisms is ``obvious'' in some sense; the other one is the
idea that almost all reasoning in CT is diagrammatical, and that as
soon as we are past the beginner stage the diagrams become ``obvious''
too: they are omitted from the books and articles for reasons of
space, but drawing the ``missing diagrams'' is something that is
almost automatic.

In this talk I will present some techniques for drawing the ``missing
diagrams'' in a more or less canonical way, and for starting from a
``skeleton'' of a categorical concept or proof and reconstructing the
rest from that.

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