---- > [!definition] Definition. ([[section]]) > Let $\mathsf{C}$ be a [[category]] and $f:A \to B$ a morphism in $\mathsf{C}$. A **section** of $f$ is a morphism $g:B \to A$ that is a right-inverse morphism: $f \circ g=1_{A}$. > > The most important example occurs in categories whose objects are sets and morphisms are (types of) functions, where a section of a map $f:X \to Y$ is a function $s: X \to Y$ satisfying $f \circ s=\id_{Y}$. ^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 > ```