Definition

A mathematical structure that consists of a set equipped with a binary operation that may not be defined for all pairs of elements, but is associative and includes identities and inverses.

Example

In category theory, a groupoid is used to study symmetries and transformations.

Conversation

Have you ever heard of a groupoid?

Yeah, I think it's related to abstract algebra, right?

Exactly! It's fascinating how it has a set with a partial binary operation.

I know, it really shows how complex mathematics can be.

Synonyms & Antonyms

Root Explanation

Groupoid → It is formed from "group" (from Latin *groupus*, meaning a collection or assembly) and "-oid" (from Greek *eidos*, meaning form or shape). The term "groupoid" refers to a mathematical structure that resembles a group but is more general, indicating a form or structure of a collection.

Memory Tip

Think of a 'group' as a collection and '-oid' as indicating a form. This helps you remember that a groupoid is a structure that resembles a group.

Visually Confused Words