Internal Diagrams in Category Theory

Internal Diagrams in Category Theory

[Eduardo Ochs]

Hello,

I think that following preprint might be of interest to some
people on the list:

   Title: Internal Diagrams in Category Theory
   Abstract: We can regard operations that discard information, like
     specializing to a particular case or dropping the intermediate
     steps of a proof, as _projections_, and operations that
     reconstruct information as _liftings_. By working with several
     projections in parallel we can make sense of statements like
     "$\Set$ is the archetypal Cartesian Closed Category", which means
     that proofs about CCCs can be done in the "archetypal language"
     and then lifted to proofs in the general setting. The method works
     even when our archetypal language is diagrammatical, has potential
     ambiguities, is not completely formalized, and does not have
     semantics for all terms. We illustrate the method with an example
     from hyperdoctrines and another from synthetic differential
     geometry.

It is at:
   http://angg.twu.net/LATEX/2010diags.pdf

Best wishes to all,
   Eduardo Ochs
   eduardoochs@gmail.com
   http://angg.twu.net/


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