Changes-note. Changed the already existing page 201707071634 to now contain a different svg illustration, planned to be used in an integrated way in pasting schemes soon.
Metadata. Like here, except that in 201707071634 symbols (arrows) indicating what is to be interpreted to 2-cells are given, in the same direction as in Power’s paper.
]]>You know that I am attempting to prove that categories Fcd and Rld defined by myself are cartesian closed.
My former attempt to prove it failed. I followed the pattern of the category of digraphs. But today I have found that there are troubles in my way to define cartesian product in the category of digraphs. (Previously I have skipped proving it, as considered it too trivial. That was my error.)
Now I realize that I have some trouble to specify exponential object, evaluation, and transpose for so simple thing as the category of digraphs.
This was probably the reason why I haven’t yet proved that Fcd and Rld are cartesian closed.
I ask for help proving that the category of digraphs is cartesian closed. Sorry for my stupidity, but it appeared not quite trivial.
See my exact question at math.stackexchange.com.
Note that I define a digraph as a relation on a set, so there are at most one edge between any two vertexes.
]]>