A homotopy of pairs gives a relative chain homotopy: 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 proved3Proved, and every prerequisite is fully proved too.

graph LR n0["Relative singular chains and homology"]:::fully_proved n1["A topological homotopy gives a singular-chain homotopy"]:::mathlib n2["A homotopy of pairs gives a relative chain homotopy"]:::fully_proved n3("Homotopic maps of pairs induce the same relative-homology map"):::fully_proved n2 -.-> n3 n0 --> n3 n0 --> n2 n1 -.-> n2 click n0 "../../../../../roadmap/homology/simplicial-and-singular/relative-homology/index.html#relative-singular-homology" "Relative singular chains and homology — 1 item · 1 fully proved" click n1 "../../../../../roadmap/homology/simplicial-and-singular/index.html#topological-homotopy-chain-homotopy" "A topological homotopy gives a singular-chain homotopy — 1 item · 1 in mathlib" class n2 focus click n2 "../../../../../roadmap/homology/simplicial-and-singular/relative-homology/index.html#relative-singular-chain-homotopy" "A homotopy of pairs gives a relative chain homotopy — 1 item · 1 fully proved" click n3 "../../../../../roadmap/homology/simplicial-and-singular/relative-homology/index.html#relative-homology-homotopy-invariance" "Homotopic maps of pairs induce the same relative-homology map — 1 item · 1 fully proved"