Relative chains commute with coproducts of arbitrary pairs: 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 proved3Proved, and every prerequisite is fully proved too.ready to state1Prerequisites are stated, so this can be written down.planned1Described in the blueprint only.

graph LR n0["Relative singular chains and homology"]:::fully_proved n1["The coproduct of a family of topological pairs"]:::fully_proved n2["Relative singular chains commute with topological coproducts"]:::fully_proved n3["Relative chains commute with coproducts of arbitrary pairs"]:::can_state n4["Relative homology commutes with coproducts of arbitrary pairs"]:::planned n3 --> n4 n1 --> n3 n2 -.-> n3 n0 --> n3 n0 --> 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/computations-and-applications/local-degree/index.html#sigma-topological-pair" "The coproduct of a family of topological pairs — 1 item · 1 fully proved" click n2 "../../../../../roadmap/homology/computations-and-applications/post-excision-applications/index.html#singular-relative-chains-coproduct" "Relative singular chains commute with topological coproducts — 1 item · 1 fully proved" class n3 focus click n3 "../../../../../roadmap/homology/computations-and-applications/local-degree/index.html#relative-chains-sigma-pair" "Relative chains commute with coproducts of arbitrary pairs — 1 item · 1 ready to state" click n4 "../../../../../roadmap/homology/computations-and-applications/local-degree/index.html#relative-homology-sigma-pair" "Relative homology commutes with coproducts of arbitrary pairs — 1 item · 1 planned"