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Lie groupoid: Measurement, Definition and basic concepts & Important classes of Lie groupoids
In mathematics, a Lie groupoid is a groupoid where the set Ob {\displaystyle \operatorname {Ob} } of objects and the set Mor {\displaystyle \operatorname {Mor} } of morphisms are both manifolds, all the category operations (source and target, composition, identity-assigning map and inversion) are smooth, and the source and target operations
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Lie groupoid topic overview
The analysis highlights Measurement, Definition and basic concepts and Important classes of Lie groupoids as prominent areas in the source structure around Lie groupoid.
Related topics
89
Source areas
7
Connected nodes
96
Extracted relationships
124
Concept neighborhoods
39
Bridge connections
96
What this topic covers Research coverage
Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.
Definition and basic concepts · 29 topics
Important classes of Lie groupoids · 16 topics
Overview · 13 topics
Examples · 12 topics
Further related concepts · 11 topics
Books · 4 topics
Morita equivalence · 4 topics
Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.
Key facts & relationships
High-confidence facts extracted from structured source data. Use them as anchors for further research.
Explore all related topics Closing gaps
A structured outline of related entities, concepts and subtopics. Open any item to build a new map centered on it.
Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.
Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.
How Lie groupoid connects Entity context
Entity context groups extracted connections by relationship type. Counts show recurrence in the analyzed source; the examples are research signals, not claims about importance.
The extracted context around Lie groupoid shows recurring relationship patterns in the source. For example, Lie groupoid → American Mathematical Society, Cambridge University Press, CBO9780511615450, CBO9780511661839, CBO9781107325883, Crainic, Differential Geometry, Fernandes, Foliations, General Theory, Geometry, Groupoids, Integrability, Introduction, ISBN, Lectures, Lie Algebroids, Lie Brackets, Lie Groupoids, MacKenzie Another extracted example is Lie groupoid → Any, Diff, For, Gamma, Germ, Given, GL, Hausdorff, Hol, If, In, Lie, Mon, On, Pi, The, This. Use these groups to spot repeated connection types before inspecting the individual relationships.
Relationships are represented as Subject → Predicate → Object triples. Confidence describes extraction strength, not the real-world importance of a relationship; lower-confidence rows may be contextual rather than explicit.
TTTA extracted 124 structured relationships around Lie groupoid. Examples in this analysis include Lie groupoid → is a → groupoid where the set Ob and Lie groupoid → related to Actions and principal bundles → Recall. The table shows each extracted connection, where it came from and its confidence.
Subject
Predicate
Object
Confidence
Src
Lie groupoid
is a
groupoid where the set Ob
0.90
text
Lie groupoid
related to Actions and principal bundles
Recall
0.60
section
Lie groupoid
related to Actions and principal bundles
Accordingly
0.60
section
Lie groupoid
related to Actions and principal bundles
Lie
0.60
section
Lie groupoid
related to Actions and principal bundles
Of
0.60
section
Lie groupoid
related to Actions and principal bundles
Given
0.60
section
Lie groupoid
related to Actions and principal bundles
Equivalent
0.60
section
Lie groupoid
related to Bisections
Lie
0.60
section
Lie groupoid
related to Bisections
In
0.60
section
Lie groupoid
related to Bisections
The
0.60
section
Lie groupoid
related to Bisections
Note
0.60
section
Lie groupoid
related to Books
Weinstein
0.60
section
No triples extracted yet.
Related concept clusters Concept neighborhoods
Concept neighborhoods group terms that sit near one another in the extracted graph. They are useful for discovering adjacent language and context, but proximity does not by itself imply a factual relationship.
The concept neighborhoods around Lie groupoid bring nearby vocabulary together. In this analysis, examples include Lie, Displaystyle and Groupoids. Use the clusters to find adjacent concepts and terminology that may deserve separate research.
Lie groupoid
Lie
Displaystyle
Groupoids
Rightrightarrows
Groups
Called
Instance
Given
Smooth
Times
Bundle
Pair
lie groupoid
Lie
Displaystyle
Rightrightarrows
Groupoids
Called
Times
Groups
Given
Smooth
Bundle
Instance
Pair
groupoid
Lie
Displaystyle
Rightrightarrows
Called
Times
Given
Smooth
Bundle
Groups
Instance
Pair
Action
morphisms
Submersions
Called
Unit
Smooth
Surjective
Two
Defined
Given
-1
Principal
Rightrightarrows
Manifold
lie group
Groupoids
Rightrightarrows
Action
Groups
Called
Pair
Unit
Given
Smooth
Times
Bundle
Structure
group
Action
Pair
Unit
Times
Structure
Lie
Principal
Groupoid
Given
Isotropy
Manifold
Groupoids
lie algebroids
Groupoids
Rightrightarrows
Groups
Called
Given
Smooth
Times
Bundle
One
Group
Structure
Two
inclusion map
Smooth
Also
Proper
Morphisms
Submersions
Surjective
-1
One
Rightrightarrows
Times
Called
Two
Connections between topic areas Semantic bridges
Semantic bridges connect parts of the graph that would otherwise be more separate. A bridge is a structural signal in this analysis, not a claim that the two topic areas are equivalent.
For Lie groupoid, one of the stronger structural bridges in this analysis connects Lie groupoid with Definition and basic concepts. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.
Number of nodes, edges, triples, density and central hubs. Use it to gauge the size and connectivity of the map.
Lie groupoid
Nodes97
Edges96
Triples124
Avg. degree1.98
Density0.020619
Components1
Source & methodology
TTTA analyzes the structure around Lie groupoid to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Measurement, Definition and basic concepts & Important classes of Lie groupoids, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.
