Research any topic before you write.
Find related topics. | Discover entities. | See connections. | Build a topical map.
In mathematics, especially in category theory and homotopy theory, a groupoid (less often Brandt groupoid or virtual group) generalises the notion of group in several equivalent ways. A groupoid can be seen as a:
Examples, Definitions & Relation to groups
Explore the main themes, entities and connections around Groupoid. Start with the topic map, then use the sections below for research and deeper semantic analysis.
Start with a few of the strongest sections from the source topic. These are research directions, not a list of keywords you must use.
High-confidence facts extracted from structured source data. Use them as anchors for further research.
Browse the full topic structure. 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.
See the strongest relationship patterns around the current topic before diving into the raw triples.
Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.
displaystyle group groupoids set category morphisms morphism one groups theory action given objects equivalence -1 mathrm every isomorphic form fundamental
| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| Groupoid | is a | small category in which every morphism is an isomorphism | 0.90 | text |
| Groupoid | is a | category in which every morphism has an inverse.If | 0.90 | text |
| Groupoid | is a | small category with o b | 0.90 | text |
| Groupoid | is a | groupoid introduced by John Horton Conway acting on 13 points such that the elements fixing a point form a copy of the Mathieu group M12 | 0.90 | text |
| manifolds | instance of | Groupoids are often used to reason about geometrical objects | 0.80 | text |
| the Rubik's Cube can be modeled using group theory | instance of | then this construction can be used to form a presheaf of groupoids.PuzzlesWhile puzzles | 0.80 | text |
| the Rubik's Cube can be modeled using group theory | instance of | PuzzlesWhile puzzles | 0.80 | text |
| Groupoid | related to Algebraic | Precisely | 0.60 | section |
| Groupoid | related to Algebraic | Here | 0.60 | section |
| Groupoid | related to Algebraic | The | 0.60 | section |
| Groupoid | related to Algebraic | For | 0.60 | section |
| Groupoid | related to Category of groupoids | The | 0.60 | section |
These clusters group vocabulary that occurs around closely connected concepts in the source material.
Bridges can reveal useful research angles that are easy to miss in a flat list of related terms.