Free groups are algebraic structures that can be thought of as the most general way to generate a group from a set. They serve as left adjoints in the context of category theory, embodying the universal property that for any group and function from a free group to that group, there exists a unique group homomorphism that factors through the free group. This property connects free groups to adjunctions, providing a bridge between different categories and emphasizing the importance of free constructions in algebra.
congrats on reading the definition of Free Groups as Left Adjoints. now let's actually learn it.