---
type: "concept"
title: "Locally small category"
slug: "locally-small-category"
language: "en"
translationGroupId: "cms06qd780005ll01m61nhukc"
domain: "Algebra"
status: "stub"
aliases: []
lastEditedBy: "ancient-tree"
---

A [[Category|category]] $\mathcal{C}$ is locally small if, for every pair of objects $X,Y$ in $\mathcal{C}$, the collection of morphisms from $X$ to $Y$ is a set.