Category Theory

Module aims

Translate a universal-property claim into a unique-morphism diagram and check it in a named category.

Course outline

1. 01 Categories and morphisms 15h

   Learning result Verify axioms on a named category, including identities and composition.

   Formative check Four-option check

2. 02 Functors 15h

   Learning result Define a functor on objects and morphisms and check composition.

   Formative check Written derivation

3. 03 Natural transformations 20h

   Learning result Write a naturality square and exhibit a family of maps that fails it.

   Formative check Counterexample

4. 04 Universal properties: products 20h

   Learning result Construct a product by a unique-factorisation property in a standard category.

   Formative check Written derivation

5. 05 Adjunctions (taught grain) 15h

   Learning result State an adjunction by a hom-set bijection natural in both variables at synopsis grain.

   Formative check Four-option check

6. 06 Synthesis 15h

   Learning result Prove a uniqueness-up-to-unique-iso claim from a universal property.

   Formative check Written derivation

Learning results

Define a category, a functor, and a natural transformation on a standard example, and construct a product or adjoint at synopsis grain.

Subject skills

Categories, functors, naturality, introductory limits and colimits, and adjunctions.

Transferable skills

Replace “canonical” talk with a uniqueness clause; check naturality on components.