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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeNov 2nd 2012
• (edited Nov 2nd 2012)

I edited the old entry projection a little.

There is no real systematics in common use of “projection” as opposed to “projector”, but I think the following makes good sense:

1. a projection is a canonical map out of a product;

2. a projector is an idempotent in a suitably abelian category

and then the relation is: A projector is a projection followed by a subobject inclusion.

That’s how I have now put it in the entry.

• CommentRowNumber2.
• CommentAuthorzskoda
• CommentTimeNov 2nd 2012

Nice remark about projector vs. projection.

I find it often as projection, or even projective, operator rather than projector. For example one talks about projective measure, which is projective operator valued.

Indeed, in functional analysis they usually distinguish the self-adjoint case of projector from non-self adjoint of an idempotent. I think that the setup is not limited to abelian categories. For example, one uses the same terminology in Quillen exact categories, so I would at least say additive instead of abelian.

• CommentRowNumber3.
• CommentAuthorTobyBartels
• CommentTimeNov 2nd 2012

I already had projection operator as a wanted link at idempotent, and now I have made it wanted at projection too, and in both cases I said that it should be self-adjoint since that's how I learnt it. Probably the self-adjoint case should just be discussed in projector, but I'm not sure how to manage the terminology.