∞-groupoid

An ∞-groupoid is a fundamental structure in higher category theory and homotopy theory that generalizes the notion of a groupoid to higher dimensions. In this context, we can think of a groupoid as a category where every morphism is invertible. An ∞-groupoid extends this idea by allowing not only objects and morphisms (which we typically think of in standard category theory), but also higher-dimensional morphisms, representing "homotopies" between morphisms.