The Stacks project

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.

Comments (2)

Comment #4972 by M. Farrokhi D. G. on

The expression "A category 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 consists of a set of objects and, for each ordered pair of objects, a set whose elements are called morphisms".

Comment #5220 by on

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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