Group theory and the number of types of connected objects
The connected components functor F on a category can reveal much about . For example, how many connected objects does have?
Definition 1: C is called connected if it has exactly one component, i.e. FC = 1 (where F is the left adjoint to the inclusion I of the category of discrete objects). This is equivalent to π0C = 1, where π0 = IF.
Exercise 1: The terminal object is connected. ...