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Stream: learning: questions

Topic: Op functor

Asad Saeeduddin (May 19 2020 at 23:17):

What is the correct name for the functor that maps a category to its own opposite? Notationally I think this is written $-^{\mathbf{op}}$, but I don't know how that's pronounced.

Fabrizio Genovese (May 19 2020 at 23:41):

Asad Saeeduddin said:

What is the correct name for the functor that maps a category to its own opposite? Notationally I think this is written $-^{\mathbf{op}}$, but I don't know how that's pronounced.

I'd pronouce it "op"... I mean it's literally ready to read... :P

Reid Barton (May 20 2020 at 00:52):

$C^{\mathrm{op}}$ is certainly pronounced "C op", but that still leaves the question of what to call the functor $-^{\mathrm{op}}$ itself.

John Baez (May 20 2020 at 06:16):

I'd call it "op". I don't say it much, but I can imagine saying "The functor 'op', that maps any category to its opposite...."