SESSION 34

*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* π_{0}C = 1, *where* π_{0} = IF.

**Exercise 1:** The terminal object is connected. ...

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