Glossary of category theory

• Notes on foundations: In many expositions, the set-theoretic issues are ignored; this means, for instance, that one does not distinguish between small and large categories and that one can arbitrarily form a localization of a category. Like those expositions, this glossary also generally ignores the set-theoretic issues, except when they are relevant

• =, which is viewed as a category
• Cat, the category of categories, where the objects are categories and the morphisms functors.
• Fct, the functor category: the category of functors from a category C to a category D.
• Set, the category of sets.
• sSet, the category of simplicial sets.
• "weak" instead of "strict" is given the default status; e.g., "n-category" means "weak n-category", not the strict one, by default.
• By an ∞-category, we mean a quasi-category, the most popular model, unless other models are being discussed.
• The number zero 0 is a natural number.

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