The good-pair quotient comparison 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

fully proved10Proved, and every prerequisite is fully proved too.

graph LR n0["Good pairs and neighborhood deformation retracts"]:::fully_proved n1["Functorial point quotients of topological pairs"]:::fully_proved n2("Good-pair relative homology is reduced quotient homology"):::fully_proved n3("The pointed relative-to-reduced comparison is natural"):::fully_proved n4["The good-pair quotient comparison is natural"]:::fully_proved n5("The zero face induces an isomorphism in relative homology"):::fully_proved n6("The first simplex computes homology relative to the second"):::fully_proved n7("Reduced homology of a wedge is the direct sum of the summands"):::fully_proved n8("The good-pair quotient exact sequence"):::fully_proved n9("Naturality of the good-pair quotient sequence"):::fully_proved n5 -.-> n6 n0 --> n2 n0 --> n4 n8 --> n9 n2 -.-> n6 n2 -.-> n5 n2 --> n4 n4 -.-> n6 n4 -.-> n5 n4 -.-> n7 n4 --> n8 n4 -.-> n9 n1 --> n2 n1 --> n4 n3 -.-> n7 n3 -.-> n9 n3 --> n4 click n0 "../../../../../../roadmap/homology/simplicial-and-singular/relative-homology/good-pair-quotient/index.html#good-pair-data" "Good pairs and neighborhood deformation retracts — 1 item · 1 fully proved" click n1 "../../../../../../roadmap/homology/simplicial-and-singular/relative-homology/good-pair-quotient/index.html#point-quotient-functor" "Functorial point quotients of topological pairs — 1 item · 1 fully proved" click n2 "../../../../../../roadmap/homology/simplicial-and-singular/relative-homology/good-pair-quotient/index.html#good-pair-point-quotient-relative-homology" "Good-pair relative homology is reduced quotient homology — 1 item · 1 fully proved" click n3 "../../../../../../roadmap/homology/simplicial-and-singular/relative-homology/good-pair-quotient/index.html#pointed-relative-reduced-homology-naturality" "The pointed relative-to-reduced comparison is natural — 1 item · 1 fully proved" class n4 focus click n4 "../../../../../../roadmap/homology/simplicial-and-singular/relative-homology/good-pair-quotient/index.html#good-pair-quotient-comparison-naturality" "The good-pair quotient comparison is natural — 1 item · 1 fully proved" click n5 "../../../../../../roadmap/homology/computations-and-applications/post-excision-applications/index.html#standard-simplex-zero-face-relative-homology" "The zero face induces an isomorphism in relative homology — 1 item · 1 fully proved" click n6 "../../../../../../roadmap/homology/computations-and-applications/post-excision-applications/index.html#double-simplex-relative-comparison" "The first simplex computes homology relative to the second — 1 item · 1 fully proved" click n7 "../../../../../../roadmap/homology/computations-and-applications/post-excision-applications/index.html#wedge-reduced-homology" "Reduced homology of a wedge is the direct sum of the summands — 1 item · 1 fully proved" click n8 "../../../../../../roadmap/homology/simplicial-and-singular/relative-homology/good-pair-quotient/index.html#good-pair-point-quotient-exact-sequence" "The good-pair quotient exact sequence — 1 item · 1 fully proved" click n9 "../../../../../../roadmap/homology/simplicial-and-singular/relative-homology/good-pair-quotient/index.html#good-pair-point-quotient-sequence-naturality" "Naturality of the good-pair quotient sequence — 1 item · 1 fully proved"