Friday, March 10, 2006

categorical nonsense

"3.1. The language of categories is affectionately known as abstract nonsense. This
is essentially accurate, and not necessarily derogatory: categories refer to nonsense
in the sense that they are all about the ‘structure’, and not about the ‘meaning’, of
what they represent. The emphasis is less on how you run into a specific set you
are looking at, and more on how that set may sit in relationship with all other sets.
Worse (or better) still, the emphasis is less on studying sets, and functions between
sets, than on studying ‘things, and things that go from things to things’ without
necessarily being explicit about what these things are: they may be sets, or groups,
or rings, or vector spaces, or modules, or other objects that are so exotic that the
reader has no right whatsoever to know about them (yet). "

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