---- > [!definition]+ Definition. ([[pointed set]]) > A **pointed set** is an ordered pair $(S,s)$, where $S$ is a set and $s \in S$ is an element of $S$, called the **basepoint**. That is, a pointed set is an object in the [[coslice category]] on a fixed singleton, $\mathsf{Set}^{\{ * \}}$. > ![[coslice category#^basic-example]] ^definition ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` #reformatrevisebatch02