04.5 Examples
4.5 Examples: Groups, Spaces, Graphs Structural thinking becomes clearer through examples. This section shows how the same principles appear in different areas. We focus on three domains: groups, topological spaces, and graphs. Each has its own objects, morphisms, invariants, and classification problems. 1. Groups A group is a set $G$ with a binary operation satisfying associativity, identity, and inverses. Objects and maps Objects: groups $(G, \ast)$ Morphisms: group homomorphisms $$...