Locally small category

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Definition

Symbol-free definition

A category is termed locally small if, for any two objects in the category, the collection of morphisms between those two objects is a set.

Definition with symbols

A category ${\mathcal {C}}$ is termed locally small if, for any objects $A,B\in \operatorname {Ob} {\mathcal {C}}$, the collection ${\mathcal {C}}(A,B)$ is a set.

Relation with other properties

Stronger properties

• Small category
• Concretizable category