Section 2.3 (0005): Categories—The Stacks project

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2.3 Categories

A category $\mathcal{C}$ consists of a set of objects and, for each pair of objects, a set of morphisms between them. In other words, it is what is called a “small” category in other texts. We will use “big” categories (categories whose objects form a proper class) as well, but only those that are listed in Categories, Remark 4.2.2.

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Comment #4972 by M. Farrokhi D. G. on March 05, 2020 at 06:44

The expression "A category $\mathcal{C}$ consists of a set of objects and, for each pair of objects, a set of morphisms between them" looks confusing specially for beginners. Should it it read "A category $\mathcal{C}$ consists of a set of objects and, for each ordered pair of objects, a set whose elements are called morphisms".

Comment #5220 by Johan on June 11, 2020 at 10:00

This is just the introduction so the language is a bit loose. Going to leave as is for now unless more people complain.

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2.3 Categories

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