>**Puzzle 132.** For any category \$$\mathcal{C}\$$, what's another name for a functor \$$F: \mathbf{1} \to \mathcal{C}\$$? There's a simple answer using concepts you've already learned in this course.

Since the category \$$\mathbf{1} \$$ is just a one object category with a single identity morphism, \$$F: \mathbf{1} \to \mathcal{C}\$$ must send this object to a single object in \$$\mathcal{C}\$$. In other words, functors \$$F: \mathbf{1} \to \mathcal{C}\$$ are objects of \$$\mathcal{C}\$$.

>**Puzzle 133.** For any category \$$\mathcal{C}\$$, what's another name for a functor \$$F: \mathbf{2} \to \mathcal{C}\$$? Again, there's a simple answer using concepts you've already learned here.

Since the category \$$\mathbf{2} \$$ is a two object category with a single non-identity morphism, \$$F: \mathbf{2} \to \mathcal{C}\$$ must send this arrow, and it's source and target objects, to a single arrow with mapped source anf target obects in \$$\mathcal{C}\$$. In other words, functors \$$F: \mathbf{2} \to \mathcal{C}\$$ are morphisms of \$$\mathcal{C}\$$.

>**Puzzle 134.** For any category \$$\mathcal{C}\$$, what's another name for a natural transformation \$$\alpha : F \Rightarrow G\$$ between functors \$$F,G: \mathbf{1} \to \mathcal{C}\$$? Yet again there's a simple answer using concepts you've learned here.

Since both \$$F\$$ and \$$G\$$ map a single set to a chosen basepoints in \$$\mathcal{C}\$$, so a natural transformation is a map that takes basepoints to basepoints, ie a based map, or point-preserving map.

>**Puzzle 135.** For any category \$$\mathcal{C}\$$, what are functors \$$F : \mathcal{C} \to \mathbf{1} \$$ like?

Such functors map all objects into a single object and maps all morphisms into the identity morphism.

>**Puzzle 138.** For any category, what are functors \$$F : \mathbf{0} \to \mathcal{C}\$$ like?

Well, \$$\mathbf{0}\$$ is empty, so a map \$$F : \mathbf{0} \to \mathcal{C}\$$ just "pops" \$$\mathcal{C}\$$ out of nothing. This mind as well be called *creatio ex nihilo,* since \$$\mathcal{C}\$$ is created out of nothingness.

>**Puzzle 139.** For any category, what are functors \$$F : \mathcal{C} \to \mathbf{0} \$$ like?

Such a map is as if \$$\mathcal{C}\$$ just vanishes from existence as if it never existed. If my Latin isn't bad, this would be *destructio in nihilio*.
Also, what \$$\mathcal{C}\$$?