Course
Category Theory
Verifying the laws that define categories, functors and natural transformations, and locating the failure when a mapping does not satisfy them.
Finishing this course means you have demonstrated the required skills with the level of support this course currently assesses.
- Modules
- 1
- Lessons
- 1
- Skills
- 2
- Starting here
- Assumes 2 prior topics
The route
Module 1: Categories, functors and naturality
The category axioms and how they are checked, the two functor laws and a composite that satisfies the object and endpoint conditions without preserving composition, and naturality as an equation required to hold at every arrow.
- Given a small category and a proposed functor between two of them, the learner can check associativity and the identity laws on every composable case, and check both functor laws on every composable pair.
- Given a mapping that is not a functor, or a family of arrows that is not natural, the learner can identify the specific law and the specific composite that breaks it, and distinguish a law failure from a mapping whose arrows have the wrong endpoints.
What finishing means
Finishing this course means you have demonstrated the required skills with the level of support this course currently assesses.
2 required skills. If you reach a lesson without the background it assumes, you are pointed at the prerequisite first, and returned here afterwards.
How progress is measured
Progress is inferred from evidence you produce, not from pages you have opened. Each required skill moves through states as evidence accumulates: met, practicing with help, performed unassisted, then performed again after a delay.
This course counts a skill as finished atguided. Where the system cannot admit evidence for a stronger claim — for instance when the only available scoring is your own judgment of your written answer — the skill stays at the state the evidence supports, and the reason is shown rather than hidden.