Superkategorio

Superkategorio, also known as supercategory, is a concept in category theory, a branch of mathematics. It is a generalization of the category concept, allowing for more complex structures and relationships. In a supercategory, objects and morphisms can themselves be categories, and the composition of morphisms is not necessarily associative. This allows for a more flexible and abstract framework for studying mathematical structures.

Supercategories were first introduced by Ross Street in the 1970s as a way to study higher-dimensional category theory. They have since been used in various areas of mathematics, including homotopy theory, higher category theory, and algebraic geometry. The concept of a supercategory is closely related to that of a bicategory, which is a category where the morphisms are themselves categories.

One of the key features of supercategories is their ability to model higher-dimensional structures. In a supercategory, a 2-morphism can be thought of as a morphism between morphisms, and a 3-morphism as a morphism between 2-morphisms, and so on. This allows for a more intuitive and natural way to study higher-dimensional phenomena.

Supercategories have also been used to study the concept of a higher-dimensional category, which is a category where the morphisms are themselves categories, and the composition of morphisms is not necessarily associative. This concept is closely related to that of a higher-dimensional category, which is a category where the morphisms are themselves categories, and the composition of morphisms is not necessarily associative.