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Comma categories are pretty expressive construction but apparently many mathematicians including their inventor, Dr. Lawvere, dislike the term for its non-informativeness. I was wondering if anyone would know of other intuitive nicknames for comma categories.

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For "slice" categories I think saying, "the category over $A$" is informative. In general, I don't know. –  Dylan Moreland Jul 2 '12 at 21:13
Knowing very little about category theory, but having looked at the Wikipedia article, if I understand correctly, the basic idea is to use morphisms as objects. Therefore "morphism category" looks like a good name to me (assuming it doesn't already have a different meaning). –  celtschk Jul 2 '12 at 21:32
Would en.wikipedia.org/wiki/Pythagorean_comma have anything to do with the naming convention? –  Fred Kline Jul 2 '12 at 21:55
I would have been utterly amazed if Pythagorean Comma could lend some intuition to the construction of comma category, but I thing there is lot more going on. –  user34942 Jul 2 '12 at 22:06
@celtschk Morphism category can be construed to mean the category $\mathcal{C}^{\mathbf{2}}$ of arrows and commutative squares in $\mathcal{C}$. –  Zhen Lin Jul 2 '12 at 22:32

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