2Morphismen

2Morphismen are concepts in mathematics that describe certain kinds of structure-preserving maps between morphisms. In category theory, a branch of mathematics that studies relationships between objects, morphisms are the arrows that connect objects. 2Morphismen, also referred to as 2-arrows or morphisms of morphisms, are the arrows that connect these morphisms.

A 2Morphism between two morphisms f and g is a way of comparing f and g, or more specifically, a way to relate the compositions of these morphisms. In more technical terms, a 2Morphism between f and g is a morphism from g to f such that the composition of this 2Morphism with g is equal to the composition of the identity morphism on f with f. The term "2" in 2Morphismen implies that these morphisms are arrows between the arrows, creating a higher-order structure.

2Morphismen find applications in many areas of mathematics, particularly in homological algebra and quasi-categories. In these contexts, 2Morphismen are used to study and compare the properties of morphisms. They are essential tools in various mathematical frameworks, such as bicategories and double categories, which allow for a more nuanced understanding of relationships between objects and their morphisms.

The study of 2Morphismen and other higher-order structures is ongoing and has led to important advancements in our understanding of mathematical relationships. Continuing research focuses on developing theoretical foundations and practical applications of these concepts.