A morphism is an arrow connecting two objects in a category. Write a morphism from A to B as A→B: it represents a permitted way to get from one object to another. Every object has an identity morphism to itself, and composing A→B with B→C yields A→C. section 7.1
A three-object category
Choose 0, 1, and 2 as objects, and draw an arrow from each number to every number greater than or equal to it. The six resulting morphisms include the three identity arrows and the arrows from 0 to 1 and 2 and from 1 to 2. section 7.1
In programming-language categories, assignment compatibility supplies a practical kind of morphism: an expression of type X may be assigned to a variable of type Y. This viewpoint connects morphisms with covariance, contravariance, functors, and type-system design. section 7.4
