Maybe these are very basic questions or I have neglected something, but I'm a bit confused by the two requirements in the definition of "enriched category", i.e. \$$I\leq\mathcal{X}(x,x) \$$ and \$$\mathcal{X}(x,y)\otimes\mathcal{X}(y,z)\leq\mathcal{X}(x,z) \$$. First, why does the definition use "≤" instead of "=" or "≥"? Second, why does the relationship between \$$\mathcal{X}(x,x) \$$ and \$$I \$$ matter (such that it must be written into the definition)?