The binary-cover Mayer–Vietoris chain complex: 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

in mathlib1Upstreamed into Mathlib.fully proved4Proved, and every prerequisite is fully proved too.

graph LR n0["The singular chain complex"]:::mathlib n1("Iterated subdivision eventually makes every singular simplex small"):::fully_proved n2["The binary-cover Mayer–Vietoris chain complex"]:::fully_proved n3("Binary-cover chains form a short exact sequence"):::fully_proved n4("Augmented binary-cover chains form a short exact sequence"):::fully_proved n2 --> n4 n2 --> n3 n3 -.-> n4 n1 --> n2 n0 --> n2 click n0 "../../../../../roadmap/homology/simplicial-and-singular/index.html#singular-chain-complex" "The singular chain complex — 1 item · 1 in mathlib" click n1 "../../../../../roadmap/homology/simplicial-and-singular/relative-homology/small-chains-and-excision/index.html#eventually-small-singular-simplices" "Iterated subdivision eventually makes every singular simplex small — 1 item · 1 fully proved" class n2 focus click n2 "../../../../../roadmap/homology/computations-and-applications/mayer-vietoris/index.html#binary-cover-chain-complex" "The binary-cover Mayer–Vietoris chain complex — 1 item · 1 fully proved" click n3 "../../../../../roadmap/homology/computations-and-applications/mayer-vietoris/index.html#binary-cover-chain-short-exact-sequence" "Binary-cover chains form a short exact sequence — 1 item · 1 fully proved" click n4 "../../../../../roadmap/homology/computations-and-applications/mayer-vietoris/index.html#augmented-binary-cover-chain-short-exact-sequence" "Augmented binary-cover chains form a short exact sequence — 1 item · 1 fully proved"