A chain map induces a map on homology: 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 mathlib5Upstreamed into Mathlib.fully proved1Proved, 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("A short exact sequence gives an exact homology sequence"):::mathlib n3("Chain-homotopic maps induce the same homology map"):::mathlib n4("Homotopic maps induce the same singular-homology map"):::mathlib n5["A homotopy equivalence induces homology isomorphisms"]:::fully_proved n3 -.-> n4 n0 --> n3 n0 -.-> n5 n0 --> n2 n0 --> n1 n0 --> n4 n4 -.-> n5 class n0 focus 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" 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#short-exact-homology-sequence" "A short exact sequence gives an exact homology sequence — 1 item · 1 in mathlib" click n3 "../../../../roadmap/homology/simplicial-and-singular/index.html#chain-homotopy-invariance" "Chain-homotopic maps induce the same homology map — 1 item · 1 in mathlib" click n4 "../../../../roadmap/homology/simplicial-and-singular/index.html#singular-homology-homotopy-invariance" "Homotopic maps induce the same singular-homology map — 1 item · 1 in mathlib" click n5 "../../../../roadmap/homology/simplicial-and-singular/index.html#homotopy-equivalence-homology-iso" "A homotopy equivalence induces homology isomorphisms — 1 item · 1 fully proved"