Library Exercise_4_2_1_10


Require Import Utf8.

Set Implicit Arguments.

Generalizable All Variables.


Exercise 4.2.1.10

Problem

Let S = {1, 2, 3, 4} : Ob Set. What is the automorphism group of S in Set, and how many elements does this group have? What is the endomorphism monoid of S in Set, and how many elements does this monoid have?
Recall from Example 4.1.2.3 that every group has an underlying monoid U(G); is the endomorphism monoid of S the underlying monoid of the automorphism group of S?