* Internal Diagrams in Category Theory
@ 2010-11-03 0:41 Eduardo Ochs
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From: Eduardo Ochs @ 2010-11-03 0:41 UTC (permalink / raw)
To: categories
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/
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
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