Relative homology of a simplicial-set pair: 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 mathlib2Upstreamed into Mathlib.fully proved4Proved, and every prerequisite is fully proved too.

graph LR n0["A chain map induces a map on homology"]:::mathlib n1["Relative homology of a simplicial-set pair"]:::mathlib n2["The singular set of a topological pair"]:::fully_proved n3("The long exact sequence of a pair"):::fully_proved n4("Relative excision reduces to the union subcomplex"):::fully_proved n5("Relative chains of a triple form a short exact sequence"):::fully_proved n0 --> n1 n1 -.-> n3 n1 --> n2 n1 --> n4 n1 -.-> n5 click n0 "../../../../../roadmap/homology/simplicial-and-singular/index.html#chain-map-homology" "A chain map induces a map on homology — 1 item · 1 in mathlib" class n1 focus click n1 "../../../../../roadmap/homology/simplicial-and-singular/relative-homology/index.html#simplicial-pair-relative-homology" "Relative homology of a simplicial-set pair — 1 item · 1 in mathlib" click n2 "../../../../../roadmap/homology/simplicial-and-singular/relative-homology/index.html#singular-pair-functor" "The singular set of a topological pair — 1 item · 1 fully proved" click n3 "../../../../../roadmap/homology/simplicial-and-singular/relative-homology/index.html#pair-long-exact-sequence" "The long exact sequence of a pair — 1 item · 1 fully proved" click n4 "../../../../../roadmap/homology/simplicial-and-singular/relative-homology/small-chains-and-excision/index.html#relative-chain-union-devissage" "Relative excision reduces to the union subcomplex — 1 item · 1 fully proved" click n5 "../../../../../roadmap/homology/simplicial-and-singular/relative-homology/index.html#triple-chain-short-exact-sequence" "Relative chains of a triple form a short exact sequence — 1 item · 1 fully proved"