The pointed relative-to-reduced 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. fully proved8Proved, and every prerequisite is fully proved too.
graph LR
n0["Relative homology at a basepoint is reduced homology"]:::fully_proved
n1("The reduced pair long exact sequence is natural"):::fully_proved
n2("The pointed relative-to-reduced comparison is natural"):::fully_proved
n3["The good-pair quotient comparison is natural"]:::fully_proved
n4["A contractible subspace identifies reduced and relative homology"]:::fully_proved
n5("The double-simplex difference generates reduced homology"):::fully_proved
n6("Reduced homology of a wedge is the direct sum of the summands"):::fully_proved
n7("Naturality of the good-pair quotient sequence"):::fully_proved
n4 -.-> n5
n3 -.-> n6
n3 -.-> n7
n2 --> n4
n2 -.-> n5
n2 -.-> n6
n2 -.-> n7
n2 --> n3
n0 --> n6
n0 --> n2
n1 -.-> n7
n1 -.-> n2
click n0 "../../../../../../roadmap/homology/simplicial-and-singular/relative-homology/index.html#pointed-relative-reduced-homology" "Relative homology at a basepoint is reduced homology — 1 item · 1 fully proved"
click n1 "../../../../../../roadmap/homology/simplicial-and-singular/relative-homology/index.html#reduced-pair-long-exact-sequence-naturality" "The reduced pair long exact sequence is natural — 1 item · 1 fully proved"
class n2 focus
click n2 "../../../../../../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"
click n3 "../../../../../../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 n4 "../../../../../../roadmap/homology/computations-and-applications/post-excision-applications/index.html#contractible-subspace-relative-reduced-homology" "A contractible subspace identifies reduced and relative homology — 1 item · 1 fully proved"
click n5 "../../../../../../roadmap/homology/computations-and-applications/post-excision-applications/index.html#double-simplex-fundamental-class" "The double-simplex difference generates reduced homology — 1 item · 1 fully proved"
click n6 "../../../../../../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 n7 "../../../../../../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"