Affine barycentric subdivision is compatible with faces: 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 proved4Proved, and every prerequisite is fully proved too.

graph LR n0("Affine barycentric subdivision is compatible with faces"):::fully_proved n1["Affine-chain subdivision is homotopic to the identity"]:::fully_proved n2["Singular-chain subdivision is naturally homotopic to the identity"]:::fully_proved n3("Barycentric subdivision contracts simplex diameter"):::fully_proved n0 --> n1 n0 --> n3 n0 --> n2 n1 -.-> n2 class n0 focus click n0 "../../../../../../roadmap/homology/simplicial-and-singular/relative-homology/small-chains-and-excision/index.html#affine-barycentric-subdivision" "Affine barycentric subdivision is compatible with faces — 1 item · 1 fully proved" click n1 "../../../../../../roadmap/homology/simplicial-and-singular/relative-homology/small-chains-and-excision/index.html#affine-chain-subdivision-homotopy" "Affine-chain subdivision is homotopic to the identity — 1 item · 1 fully proved" click n2 "../../../../../../roadmap/homology/simplicial-and-singular/relative-homology/small-chains-and-excision/index.html#singular-chain-subdivision-homotopy" "Singular-chain subdivision is naturally homotopic to the identity — 1 item · 1 fully proved" click n3 "../../../../../../roadmap/homology/simplicial-and-singular/relative-homology/small-chains-and-excision/index.html#barycentric-subdivision-diameter" "Barycentric subdivision contracts simplex diameter — 1 item · 1 fully proved"