The kernel is generated by overlap relations: local context

Project map · Chapter map · Full theorem DAG · Open textbook statement

This local map shows one dependency hop in either direction. The highlighted item is the current focus. What the colours mean

fully proved5Proved, and every prerequisite is fully proved too.

graph LR n0["The group presentation associated to an open cover"]:::fully_proved n1("Overlap relations vanish under the cover map"):::fully_proved n2("Homotopic factorizations have the same quotient class"):::fully_proved n3("The kernel is generated by overlap relations"):::fully_proved n4["Van Kampen's quotient isomorphism"]:::fully_proved n0 --> n1 n0 --> n2 n0 --> n3 n1 -.-> n3 n1 --> n4 n2 -.-> n3 n3 -.-> n4 click n0 "../../../../roadmap/fundamental-group/van-kampen/index.html#cover-group-presentation" "The group presentation associated to an open cover — 1 item · 1 fully proved" click n1 "../../../../roadmap/fundamental-group/van-kampen/index.html#cover-map-relations" "Overlap relations vanish under the cover map — 1 item · 1 fully proved" click n2 "../../../../roadmap/fundamental-group/van-kampen/index.html#homotopic-factorizations" "Homotopic factorizations have the same quotient class — 1 item · 1 fully proved" class n3 focus click n3 "../../../../roadmap/fundamental-group/van-kampen/index.html#van-kampen-kernel" "The kernel is generated by overlap relations — 1 item · 1 fully proved" click n4 "../../../../roadmap/fundamental-group/van-kampen/index.html#van-kampen-quotient" "Van Kampen's quotient isomorphism — 1 item · 1 fully proved"