Homotopic factorizations have the same quotient class: 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 proved6Proved, and every prerequisite is fully proved too.

graph LR n0["The group presentation associated to an open cover"]:::fully_proved n1["Cover factorizations of a loop"]:::fully_proved n2("Elementary factorization moves preserve the quotient class"):::fully_proved n3("A homotopy admits a threefold-incidence cover decomposition"):::fully_proved n4("Homotopic factorizations have the same quotient class"):::fully_proved n5("The kernel is generated by overlap relations"):::fully_proved n1 --> n2 n1 --> n4 n0 --> n1 n0 --> n2 n0 --> n4 n0 --> n5 n2 -.-> n4 n4 -.-> n5 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-factorization" "Cover factorizations of a loop — 1 item · 1 fully proved" click n2 "../../../../roadmap/fundamental-group/van-kampen/index.html#factorization-moves" "Elementary factorization moves preserve the quotient class — 1 item · 1 fully proved" click n3 "../../../../roadmap/fundamental-group/van-kampen/index.html#homotopy-cover-decomposition" "A homotopy admits a threefold-incidence cover decomposition — 1 item · 1 fully proved" class n4 focus click n4 "../../../../roadmap/fundamental-group/van-kampen/index.html#homotopic-factorizations" "Homotopic factorizations have the same quotient class — 1 item · 1 fully proved" click n5 "../../../../roadmap/fundamental-group/van-kampen/index.html#van-kampen-kernel" "The kernel is generated by overlap relations — 1 item · 1 fully proved"