Test categories: 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. ready to state1Nothing it needs is blocked, so the statement can be written in Lean.planned20Described in the blueprint only.
graph LR
n0("Sheaf cohomology bounds"):::can_state
n1["Test categories"]:::planned
n2("Simplex generators"):::planned
n3("Verdier duality on test categories"):::planned
n4("Direct images and open extension"):::planned
n5("Products with the interval"):::planned
n6("Two endpoint forms"):::planned
n7("Homotopy invariance"):::planned
n8("Point groups"):::planned
n9("Cutoff"):::planned
n10("Objects supported in an open set"):::planned
n11("Witt localization"):::planned
n12("Contractible quotient"):::planned
n13("Germ description"):::planned
n14("Open cover dense inclusion"):::planned
n15("Bounded comparison"):::planned
n16("Rational sphere calculation"):::planned
n17("Signature on a finite relation"):::planned
n18("Fixed sphere lattice"):::planned
n19("Action of degree"):::planned
n20("Sign conventions"):::planned
n0 -.-> n1
n10 --> n13
n10 --> n14
n10 --> n11
n9 -.-> n10
n9 -.-> n13
n9 -.-> n14
n13 -.-> n14
n14 -.-> n15
n14 -.-> n16
n11 -.-> n15
n11 -.-> n12
n11 -.-> n16
n6 -.-> n7
n7 -.-> n15
n7 -.-> n12
n7 -.-> n19
n7 -.-> n16
n5 -.-> n6
n2 -.-> n5
n2 -.-> n3
n2 -.-> n8
n1 --> n10
n1 --> n9
n1 --> n13
n1 --> n14
n1 --> n11
n1 --> n6
n1 --> n7
n1 --> n5
n1 --> n20
n1 --> n2
n1 --> n3
n1 --> n4
n1 --> n15
n1 --> n12
n1 --> n19
n1 --> n17
n1 --> n8
n1 --> n18
n1 --> n16
n3 -.-> n10
n3 -.-> n4
n4 -.-> n10
n4 -.-> n9
n4 -.-> n14
n4 --> n7
n4 -.-> n12
n4 -.-> n19
n15 -.-> n18
n17 -.-> n18
n8 -.-> n15
n8 -.-> n12
n8 -.-> n16
n18 --> n19
n16 -.-> n17
n16 -.-> n18
click n0 "../../../roadmap/background/index.html#sheaf-cohomology-bounds" "Sheaf cohomology bounds — 1 item · 1 ready to state"
class n1 focus
click n1 "../../../roadmap/sheaf-categories/index.html#test-categories" "Test categories — 1 item · 1 planned"
click n2 "../../../roadmap/sheaf-categories/index.html#simplex-generators" "Simplex generators — 1 item · 1 planned"
click n3 "../../../roadmap/sheaf-categories/index.html#test-duality" "Verdier duality on test categories — 1 item · 1 planned"
click n4 "../../../roadmap/sheaf-categories/index.html#test-pushforward" "Direct images and open extension — 1 item · 1 planned"
click n5 "../../../roadmap/sheaf-categories/index.html#interval-products" "Products with the interval — 1 item · 1 planned"
click n6 "../../../roadmap/sheaf-categories/index.html#endpoint-forms" "Two endpoint forms — 1 item · 1 planned"
click n7 "../../../roadmap/sheaf-categories/index.html#homotopy-invariance" "Homotopy invariance — 1 item · 1 planned"
click n8 "../../../roadmap/sphere-lattice/index.html#point-groups" "Point groups — 1 item · 1 planned"
click n9 "../../../roadmap/localization/index.html#cutoff" "Cutoff — 1 item · 1 planned"
click n10 "../../../roadmap/localization/index.html#compact-support" "Objects supported in an open set — 1 item · 1 planned"
click n11 "../../../roadmap/localization/index.html#witt-localization" "Witt localization — 1 item · 1 planned"
click n12 "../../../roadmap/sphere-lattice/index.html#contractible-quotient" "Contractible quotient — 1 item · 1 planned"
click n13 "../../../roadmap/localization/index.html#germs" "Germ description — 1 item · 1 planned"
click n14 "../../../roadmap/localization/index.html#open-cover" "Open cover dense inclusion — 1 item · 1 planned"
click n15 "../../../roadmap/sphere-lattice/index.html#bounded-comparison" "Bounded comparison — 1 item · 1 planned"
click n16 "../../../roadmap/sphere-lattice/index.html#sphere-rank" "Rational sphere calculation — 1 item · 1 planned"
click n17 "../../../roadmap/sphere-lattice/index.html#generic-signature" "Signature on a finite relation — 1 item · 1 planned"
click n18 "../../../roadmap/sphere-lattice/index.html#sphere-lattice" "Fixed sphere lattice — 1 item · 1 planned"
click n19 "../../../roadmap/sphere-lattice/index.html#degree-action" "Action of degree — 1 item · 1 planned"
click n20 "../../../roadmap/sheaf-categories/index.html#sign-conventions" "Sign conventions — 1 item · 1 planned"