Groupoid

:In addition to the present meaning, the term "groupoid" is also used for a magma: a set with an arbitrary binary operation on it. This encyclopedia does not use that sense of this word.

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In mathematics, especially in category theory and homotopy theory, a groupoid is a concept (first developed by Heinrich Brandt in 1926) that simultaneously generalises groups, equivalence relations on sets, and actions of groups on sets.

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They are often used to capture information about geometrical objects such as manifolds.

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Magma: :This article is about the type of molten rock. For other meanings of magma, see Magma (disambiguation)....

Set: :This article is about sets in mathematics. For other senses, see set (disambiguation)....

Binary operation: In mathematics, a binary operation, or binary operator, is a calculation involving two input quantities. Binary operations are sometimes called dyadic operations in order to avoid confusion with the binary numeral system. Examples include the familiar arithmetic operations of addition, subtraction, ...