@JakeGillberg wrote:
> How about an "almost-category" satisfying everything but the left identity law?
Here is one based ideas from the web. Let the morphisms of our one-object category be the integers \\(\mathbb{Z}\\).
Define the binary operation by a;b = |a|*b.
It's easy to show that this is associative. (So, a semigroup.)
1 is a left identity. But there's no right identity.