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added this quote, from p. 103:
The multiple examples, here and elsewhere, of adjoint functors tend to show that adjoints occur almost everywhere in many branches of Mathematics. It is the thesis of this book that a systematic use of all these adjunctions illuminates and clarifies these subjects.
I am taking the liberty of deleting this old paragraph:
Categories Work is the standard reference for category theory, and we may often cite it here. Almost all of its terminology is widely adopted, although its approach to foundations (one Grothendieck universe) is not as widely used (see discussion at nForum).
If anyone feels strongly that there is something in the paragraph which is worth retaining, then let’s maybe try to rephrase it and put it back in.
Would anybody know if it’s possible to retrieve that old discussion (linked to in the paragraph) of #3)? The URL is for an ntnu.no page from when Andrew Stacey was around.
Re #4: Simply append the number found in the URL to https://nforum.ncatlab.org/discussion/:
I’d be in favour of keeping a slimmed down and modified version of the opening sentence, something like
Categories for the Working Mathematician has been a standard reference for category theory for decades; not the only one, but perhaps the most iconic.
We have more options pitched at different levels today, and saying CWM is the standard reference is (as I’m sure Urs was thinking, in part) too strong a statement.
I also don’t see why the book needs to referred to as ’Categories Work’ (this has never gelled with me) in a reference page. In discussions on the net, sure. But electrons are cheap, and it’s a type-roughly once situation here.
(Thank you, David.)
I’m in favor of David’s suggestion in #6, with an option of replacing “perhaps” by “one of”.
If “Categories Work” doesn’t work for David, I think we should get rid of it. (I’ve never used it in speech, I’m pretty sure, and never heard anyone who did.)
A moot point, maybe, but I’ve found the foundational axiom of one universe useful on various occasions.
I agree with Todd’s suggestion editing my sentence. If no one has added it to the page I’ll do it soon. I’ve never heard or read “Categories Work” outside the nLab, but I grant that someone must have been familiar with it, to include it here.
Wikipedia abbreviates it as CWM.
The entry does open with saying it’s a “classical reference”.
Not clear what is gained by claiming that it’s “iconic” – which sounds appropriate for a book review signed by a single author who can claim to have this subjective feeling.
Also to reflect on how much the clever title influences this feeling. Imagine Borceux had chosen a more iconic title for his “Handbook” (which, incidentally, the nLab cites much more.)
How about this:
After “…is a classical textbook on category theory”, we continue with:
The iconic title probably refers to the declared ambition of demonstrating the prevalence of examples of adjoint functors occurring throughout mathematics
[p. 2:] “Adjoints, as we shall see, occur throughout mathematics.”
followed by the other quote which was there already (#2):
[p. 103:] “The multiple examples, here and elsewhere, of adjoint functors tend to show that adjoints occur almost everywhere in many branches of Mathematics. It is the thesis of this book that a systematic use of all these adjunctions illuminates and clarifies these subjects.”
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