Infinity-Category

An infinity-category (or ∞-category) is a higher category in which the tower of morphisms continues through all finite dimensions and stabilizes in the limit, encoding a coherent notion of equivalence at every level. Unlike an n-category, which truncates after n levels of structure, an ∞-category treats homotopy as primitive: morphisms are paths, 2-morphisms are homotopies between paths, 3-morphisms are homotopies between homotopies, and the tower never ends. This makes ∞-categories the natural setting for homotopy theory, algebraic topology, and any domain where the