An indexed cone attachment is a standard cell attachment: 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 proved8Proved, and every prerequisite is fully proved too.

graph LR n0("An indexed family of cone attachments is a topological pushout"):::fully_proved n1["The cone on a disk boundary is the disk"]:::fully_proved n2["An indexed cone attachment is a standard cell attachment"]:::fully_proved n3["Every abstract cell attachment has an indexed cone model"]:::fully_proved n4["Free-group relators form a standard two-cell attachment"]:::fully_proved n5["A point is one standard zero-cell"]:::fully_proved n6["A wedge of circles is an indexed one-cell attachment"]:::fully_proved n7["The cyclic presentation complex"]:::fully_proved n1 --> n2 n2 --> n3 n2 --> n7 n2 --> n5 n2 --> n4 n2 --> n6 n0 --> n2 click n0 "../../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/index.html#indexed-cone-pushout" "An indexed family of cone attachments is a topological pushout — 1 item · 1 fully proved" click n1 "../../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/index.html#cone-disk-homeomorphism" "The cone on a disk boundary is the disk — 1 item · 1 fully proved" class n2 focus click n2 "../../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/index.html#indexed-basic-cell-attachment" "An indexed cone attachment is a standard cell attachment — 1 item · 1 fully proved" click n3 "../../../../../roadmap/fundamental-group/van-kampen/cell-attachment-support/index.html#abstract-cell-attachment-indexed-model" "Every abstract cell attachment has an indexed cone model — 1 item · 1 fully proved" click n4 "../../../../../roadmap/fundamental-group/van-kampen/presentation-complex/index.html#relator-cell-attachment" "Free-group relators form a standard two-cell attachment — 1 item · 1 fully proved" click n5 "../../../../../roadmap/fundamental-group/van-kampen/presentation-complex/index.html#point-zero-cell-attachment" "A point is one standard zero-cell — 1 item · 1 fully proved" click n6 "../../../../../roadmap/fundamental-group/van-kampen/presentation-complex/index.html#wedge-circles-one-skeleton" "A wedge of circles is an indexed one-cell attachment — 1 item · 1 fully proved" click n7 "../../../../../roadmap/fundamental-group/van-kampen/presentation-complex/index.html#cyclic-presentation-complex" "The cyclic presentation complex — 1 item · 1 fully proved"