Where does the name "slice category" originate for the category $(\mathscr{C} \downarrow C)$ of objects over $C$?
Slice category - origin of the name
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category-theory
terminology
slice-category
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0A quick search on MathSciNet tells me that the term slice category was used at least around 1980 without explanation in [this review](http://www.ams.org/mathscinet-getitem?mr=567064). – 2017-02-21
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0Perhaps [this question](https://math.stackexchange.com/questions/994256/whats-a-good-motivating-example-for-the-concept-of-a-slice-category) which provides some motivating examples will help explain the name. – 2017-02-22
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0The name comma category (which is a generalisation of a slice category) comes from the fact that it was used to be denoted with a comma ([ref](https://en.wikipedia.org/wiki/Comma_category)). A slice category is sometimes denoted as $\mathcal{C} / C$, so perhaps the term slice category comes from the $/$ symbol. – 2017-02-22