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crossed module

Relationships observed in Wikidata. Connections do not establish verification or source support.

Release: sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7

Provider: Wikidata · graph projection only.

OBSERVED · GRAPH-PROJECTION · NOT ADMITTED · NOT VERIFIED · NOT SUPPORT

Edge identity is the provider property id (for example P31). It is not a Counterpedia predicate.

Development requests are not available on this deployment. The observed entity and its graph links remain readable.

Relationships of crossed module

Show relationship types (drawing only; the text lists are unaffected)
Relationship label not yet available (Observed provider relationships)Relationship label not yet available (Observed provider relationships)Relationship label not yet available (Observed provider relationships)Relationship label not yet available (Observed provider relationships)studied by (Observed provider relationships)Relationship label not yet available (Observed provider relationships)Relationship label not yet available (Observed provider relationships)Relationship label not yet available (Observed provider relationships)Relationship label not yet available (Observed provider relationships)Relationship label not yet available (Observed provider relationships)subclass of (Observed provider relationships)studied by (Observed provider relationships)Relationship label not yet available (Observed provider relationships)crossed module — Wikidata entity (Q5188565)crossed moduleWIKIDATA ENTITY(\cdot) — Literal value (wikidata:literal:0:(\cdot))(\cdot)LITERAL VALUEhttps://mathoverflow.net/tags/crossed-modules — Literal value (wikidata:literal:1:https://mathoverflow.net/tags/crossed-modules)https://mathoverflow.net/tags/c…LITERAL VALUEJ. H. C. Whitehead — Wikidata entity (Q378553)J. H. C.WhiteheadWIKIDATA ENTITY\operatorname{Aut}(-) — Literal value (wikidata:literal:3:\operatorname{Aut}(-))\operatorname{Aut}(-)LITERAL VALUEhomotopical algebra — Wikidata entity (Q5891810)homotopicalalgebraWIKIDATA ENTITY1941 — Literal value (wikidata:literal:5:1941)1941LITERAL VALUE\begin{aligned}d\colon H&\to G \\ (\cdot)\colon G &\to \operatorname{Aut}(H) \\ d(g\cdot h) &= gd(h)g^{-1} \\ d (h)\cdot h' &= hh'h^{-1} \end{aligned} — Literal value (wikidata:literal:6:\begin{aligned}d\colon H&\to G \\ (\cdot)\colon G &\to \operatorname{Aut}(H) \\ d(g\cdot h) &= gd(h)g^{-1} \\ d (h)\cdot h' &= hh'h^{-1} \end{aligned})\begin{aligned}d\colon H&\to G…LITERAL VALUEWikiProject Mathematics — Wikidata entity (Q8487137)WikiProjectMathematicsWIKIDATA ENTITYd — Literal value (wikidata:literal:8:d)dLITERAL VALUEH — Literal value (wikidata:literal:9:H)HLITERAL VALUEalgebraic structure — Wikidata entity (Q205464)algebraicstructureWIKIDATA ENTITYhigher category theory — Wikidata entity (Q5758318)higher categorytheoryWIKIDATA ENTITYG — Literal value (wikidata:literal:12:G)GLITERAL VALUE

Legend

  • Governed record relationships (solid)
  • Countergraph traversal (dashed)
  • Countergraph evidence (dotted)
  • Observed provider relationships (dash-dot)
  • Structurally derived (sparse dots)

Node shape identifies node kind only. Size, color, and position carry no meaning beyond hop distance from the root.

A line means a supported artifact carried an explicit structured relation. It does not mean the relation is true, admitted, verified, or authoritative.

Graph as text

Nodes (14)

  • crossed module — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q5188565
    stable_ref
    Q5188565
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q5188565
    provider
    wikidata
    entity_href
    /entries/wikidata/Q5188565
  • (\cdot) — Literal value
    Technical details
    node_id
    wikidata:literal:0:(\cdot)
    stable_ref
    wikidata:literal:0:(\cdot)
    node_kind
    wikidata_literal
    plane
    provider_observed
  • https://mathoverflow.net/tags/crossed-modules — Literal value
    Technical details
    node_id
    wikidata:literal:1:https://mathoverflow.net/tags/crossed-modules
    stable_ref
    wikidata:literal:1:https://mathoverflow.net/tags/crossed-modules
    node_kind
    wikidata_literal
    plane
    provider_observed
  • J. H. C. Whitehead — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q378553
    stable_ref
    Q378553
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q378553
    provider
    wikidata
    entity_href
    /entries/wikidata/Q378553
  • \operatorname{Aut}(-) — Literal value
    Technical details
    node_id
    wikidata:literal:3:\operatorname{Aut}(-)
    stable_ref
    wikidata:literal:3:\operatorname{Aut}(-)
    node_kind
    wikidata_literal
    plane
    provider_observed
  • homotopical algebra — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q5891810
    stable_ref
    Q5891810
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q5891810
    provider
    wikidata
    entity_href
    /entries/wikidata/Q5891810
  • 1941 — Literal value
    Technical details
    node_id
    wikidata:literal:5:1941
    stable_ref
    wikidata:literal:5:1941
    node_kind
    wikidata_literal
    plane
    provider_observed
  • \begin{aligned}d\colon H&\to G \\ (\cdot)\colon G &\to \operatorname{Aut}(H) \\ d(g\cdot h) &= gd(h)g^{-1} \\ d (h)\cdot h' &= hh'h^{-1} \end{aligned} — Literal value
    Technical details
    node_id
    wikidata:literal:6:\begin{aligned}d\colon H&\to G \\ (\cdot)\colon G &\to \operatorname{Aut}(H) \\ d(g\cdot h) &= gd(h)g^{-1} \\ d (h)\cdot h' &= hh'h^{-1} \end{aligned}
    stable_ref
    wikidata:literal:6:\begin{aligned}d\colon H&\to G \\ (\cdot)\colon G &\to \operatorname{Aut}(H) \\ d(g\cdot h) &= gd(h)g^{-1} \\ d (h)\cdot h' &= hh'h^{-1} \end{aligned}
    node_kind
    wikidata_literal
    plane
    provider_observed
  • WikiProject Mathematics — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q8487137
    stable_ref
    Q8487137
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q8487137
    provider
    wikidata
    entity_href
    /entries/wikidata/Q8487137
  • d — Literal value
    Technical details
    node_id
    wikidata:literal:8:d
    stable_ref
    wikidata:literal:8:d
    node_kind
    wikidata_literal
    plane
    provider_observed
  • H — Literal value
    Technical details
    node_id
    wikidata:literal:9:H
    stable_ref
    wikidata:literal:9:H
    node_kind
    wikidata_literal
    plane
    provider_observed
  • algebraic structure — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q205464
    stable_ref
    Q205464
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q205464
    provider
    wikidata
    entity_href
    /entries/wikidata/Q205464
  • higher category theory — Wikidata entity
    Technical details
    node_id
    wikidata:entity:Q5758318
    stable_ref
    Q5758318
    node_kind
    wikidata_entity
    plane
    provider_observed
    qid
    Q5758318
    provider
    wikidata
    entity_href
    /entries/wikidata/Q5758318
  • G — Literal value
    Technical details
    node_id
    wikidata:literal:12:G
    stable_ref
    wikidata:literal:12:G
    node_kind
    wikidata_literal
    plane
    provider_observed

Edges (13)

  • crossed module — Relationship label not yet available → (\cdot) — Observed provider relationships
    Technical details
    machine_predicate
    P7235
    predicate_ref
    wikidata:property:P7235
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:0:P7235
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • crossed module — Relationship label not yet available → https://mathoverflow.net/tags/crossed-modules — Observed provider relationships
    Technical details
    machine_predicate
    P1482
    predicate_ref
    wikidata:property:P1482
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:1:P1482
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • crossed module — Relationship label not yet available → J. H. C. Whitehead — Observed provider relationships
    Technical details
    machine_predicate
    P61
    predicate_ref
    wikidata:property:P61
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:2:P61
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • crossed module — Relationship label not yet available → \operatorname{Aut}(-) — Observed provider relationships
    Technical details
    machine_predicate
    P7235
    predicate_ref
    wikidata:property:P7235
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:3:P7235
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • crossed module — studied by → homotopical algebra — Observed provider relationships
    Technical details
    machine_predicate
    P2579
    predicate_ref
    wikidata:property:P2579
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:4:P2579
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • crossed module — Relationship label not yet available → 1941 — Observed provider relationships
    Technical details
    machine_predicate
    P575
    predicate_ref
    wikidata:property:P575
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:5:P575
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • crossed module — Relationship label not yet available → \begin{aligned}d\colon H&\to G \\ (\cdot)\colon G &\to \operatorname{Aut}(H) \\ d(g\cdot h) &= gd(h)g^{-1} \\ d (h)\cdot h' &= hh'h^{-1} \end{aligned} — Observed provider relationships
    Technical details
    machine_predicate
    P2534
    predicate_ref
    wikidata:property:P2534
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:6:P2534
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • crossed module — Relationship label not yet available → WikiProject Mathematics — Observed provider relationships
    Technical details
    machine_predicate
    P6104
    predicate_ref
    wikidata:property:P6104
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:7:P6104
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • crossed module — Relationship label not yet available → d — Observed provider relationships
    Technical details
    machine_predicate
    P7235
    predicate_ref
    wikidata:property:P7235
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:8:P7235
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • crossed module — Relationship label not yet available → H — Observed provider relationships
    Technical details
    machine_predicate
    P7235
    predicate_ref
    wikidata:property:P7235
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:9:P7235
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • crossed module — subclass of → algebraic structure — Observed provider relationships
    Technical details
    machine_predicate
    P279
    predicate_ref
    wikidata:property:P279
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:10:P279
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • crossed module — studied by → higher category theory — Observed provider relationships
    Technical details
    machine_predicate
    P2579
    predicate_ref
    wikidata:property:P2579
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:11:P2579
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7
  • crossed module — Relationship label not yet available → G — Observed provider relationships
    Technical details
    machine_predicate
    P7235
    predicate_ref
    wikidata:property:P7235
    provider
    wikidata
    provider_direction
    outgoing
    plane
    provider_observed
    edge_id
    wikidata:relation:12:P7235
    release_ref
    sha256:f33228901a35b0683356002a46df9ceb11f399d05f17abb5c7c78256cbf38ba7

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