---- > [!definition] Definition. ([[chain homotopy equivalence]]) > A [[chain map]] $f_{\bullet}$ is a **chain homotopy equivalence** if there is a [[chain map]] $g_{\bullet}:D_{\bullet} \to C_{\bullet}$ and [[chain homotopy|chain homotopies]] $f_{\bullet} \circ g_{\bullet} \simeq \id_{D_{\bullet}}$ and $g_{\bullet} \circ f_{\bullet} \simeq \id_{C_{\bullet}}$. ^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 > ```