Oi lista,
acabei de subir pro Arxiv e pra minha página o texto abaixo, que acho
que pode interessar a várias pessoas daqui...
On my favorite conventions for drawing the missing diagrams in
Category Theory
I used to believe that my conventions for drawing diagrams for
categorical statements could be written down in one page or less,
and that the only tricky part was the technique for reconstructing
objects "from their names"... but then I found out that this is not
so.
This is an attempt to explain, with motivations and examples, all
the conventions behind a certain diagram, called the "Basic Example"
in the text. Once the conventions are understood that diagram
becomes a "skeleton" for a certain lemma related to the Yoneda
Lemma, in the sense that both the statement and the proof of that
lemma can be reconstructed from the diagram. The last sections
discuss some simple ways to extend the conventions; we see how to
express in diagrams the ("real") Yoneda Lemma and a corollary of it,
how to define comma categories, and how to formalize the diagram for
"geometric morphism for children".
People in CT usually only share their ways of visualizing things
when their diagrams cross some threshold of of mathematical
relevance --- and this usually happens when they prove new theorems
with their diagrams, or when they can show that their diagrams can
translate calculations that used to be huge into things that are
much easier to visualize. The diagrammatic language that I present
here lies below that threshold --- and so it is a "private"
diagrammatic language, that I am making public as an attempt to
establish a dialogue with other people who have also created their
own private diagrammatic languages.
Links:
http://angg.twu.net/math-b.html#favorite-conventions
http://angg.twu.net/LATEX/2020favorite-conventions.pdf
[[]] =),
Eduardo Ochs
http://angg.twu.net/math-b.html
http://angg.twu.net/dednat6.html
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