Exercise 3-12

  1. What is the category 1?

  2. What is the category 0?

  3. What is the formula for the number of morphisms in n?

Solution(1)

  1. It has one object and one (identity) morphism.

  2. It has zero objects and zero morphisms.

  3. \(1+2+...+n\), i.e. \(\frac{n(n+1)}{2}\)