Category theory question

  • #1

Homework Statement



Show that there are only two possible categories with one object and two morphisms.

Homework Equations



None

The Attempt at a Solution



My thinking here is as follows : Let's say that the object in our category is A, and that the two morphisms are f and 1, where 1 is the identity. Obviously they both have domain = codomain = A. So the only way that I see to make a difference between the categories is to define the composition differently, i.e. to make either ff = f or ff = 1. Is this enough to say that the two are different?
 

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