In category theory, a branch of mathematics, an initial object of a category C is an object I in C such that for every object X in C, there exists precisely one morphism I → X.
The dual notion is that of a terminal object (also called terminal element): T is terminal if for every object X in C there exists exactly one morphism X → T. Initial objects are also called coterminal or universal, and terminal objects are also called final.
If an object is both initial and terminal, it is called a zero object or null object. A pointed category is one with a zero object.
A strict initial object I is one for which every morphism into I is an isomorphism.
Total ways to arrange the 7 letters: 7! / (2! x 2!) = 1260
Ways to have an N at each end: N _ _ _ _ _ N
There are 5 other letters in the middle, and two of them repeat (U), so the middle 5 are found by 5! / 2! = 60
Now, here is where I am unsure what to do. Since the N's are identical, do...