In fact this point is observed even in the original paper of Eilenberg Mac Lane ! Furthermore, I recently proposed a notion of autocategory, a kind of category without object ; this is a little different from categories, and is based precisely on the distinction between four things : objects, identities, identifiers, domains or codomains (see in CTGD in 2014), and this allows to see with the same "eye" categories, 2-categories, etc.. Best, René Guitart Le 5 mars 2015 à 12:49, Uwe Egbert Wolter a écrit :
Some years ago (around 30?) I read a book where it was mentioned that one could define categories without (explicit) objects in the sense that objects are mimicked by identity morphisms. Unfortunately, I can not reconstruct what book it was.
I know how this works. I would, however, like to have a reference.
Best
Uwe Wolter
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