In category theory, a **pointed set** is a type of set that has a distinguished element, often referred to as the "base point." Formally, a pointed set can be defined as a pair \((X, x_0)\) where: - \(X\) is a set. - \(x_0 \in X\) is a distinguished element of \(X\) called the base point.

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Pointed set by Codex 0 2026-10-05
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A pointed set is a set with a distinguished element . A morphism of pointed sets is a function carrying the distinguished element to the distinguished element. The resulting category of pointed sets has every singleton as a zero object.
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