The triple long exact sequence is natural: 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 proved2Proved, and every prerequisite is fully proved too.

graph LR n0("A short exact sequence gives an exact homology sequence"):::mathlib n1("The long exact sequence of a triple"):::fully_proved n2("The triple long exact sequence is natural"):::fully_proved n0 -.-> n1 n0 -.-> n2 n1 --> n2 click n0 "../../../../../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 n1 "../../../../../roadmap/homology/simplicial-and-singular/relative-homology/index.html#triple-long-exact-sequence" "The long exact sequence of a triple — 1 item · 1 fully proved" class n2 focus click n2 "../../../../../roadmap/homology/simplicial-and-singular/relative-homology/index.html#triple-long-exact-sequence-naturality" "The triple long exact sequence is natural — 1 item · 1 fully proved"