infinity1categories
infinity1categories, also known as ∞-categories orinfty-categories, are a generalization of the notion of a category. In a standard category, morphisms are just arrows, and composition is associative. In an ∞-category, the "morphisms" are higher-dimensional structures, often visualized as cells or n-cells, and the composition of these higher-dimensional structures is associative up to a higher coherent homotopy. This means that composing three or more morphisms in different ways might not yield the exact same result, but rather results that are equivalent through a chain of higher-dimensional equivalences.
The formal definition of an ∞-category can be approached in several ways, including through the use of
One key concept related to ∞-categories is the idea of "homotopy coherence." In a standard category, associativity