Category Theory

By the end, you can

• Define a category and name its four components.
• State both category axioms (identity and associativity) and explain what each guarantees.
• Evaluate a composition expression by applying the right-to-left rule.
• Identify which pairs of morphisms can be composed given their domains and codomains.
• Describe the Hask category and map each categorical concept to its programming counterpart.
• Give examples of morphisms that are not functions (poset relations, monoid elements).
• Explain what a functor is and verify that a given map satisfies the two functor laws.
• Predict the result of mapping a function over a list, a non-empty optional, and an empty optional.