Horizontal Composition
Definition
Def Pasting Diagram
Given a category, a pasting diagram in is a sequence of composable morphisms:
2-Category
Definition
Def 2-Category
A 2-category is comprised of:
- A collection of
-cells, also known as objects. - A collection of
-cells, also known as -morphisms between pairs of objects: - A collection of
-cells, also known as -morphisms between parallel pairs of -morphisms : So that the following conditions hold:
- The objects and
-morphisms form a category, with identities . - For each fixed pair of objects
and , the -morphisms and -morphisms between such form a category under an operation called vertical composition with identities . - There is also a category whose objects are the objects in which a morphism from
to is a -cell under an operation called horizontal composition, with identities . - The horizontal composite
of identities for vertical composition must be the identity for the composite -morphisms. - The law of middle four interchange holds.
