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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.2012-07-02
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    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).2012-07-02
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    Would http://en.wikipedia.org/wiki/Pythagorean_comma have anything to do with the naming convention?2012-07-02
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    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.2012-07-02
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    @celtschk Morphism category can be construed to mean the category $\mathcal{C}^{\mathbf{2}}$ of arrows and commutative squares in $\mathcal{C}$.2012-07-02
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    How about something along the lines of "homotopy directed pullback"? It would be nice to call them simply lax pullbacks, but I don't think they are really equivalent...2012-07-09

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