Category Theory

模块目标

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

课程大纲

1. 01 Categories and morphisms 15h

   学习结果 Verify axioms on a named category, including identities and composition.

   形成性检查 四选一检查

2. 02 Functors 15h

   学习结果 Define a functor on objects and morphisms and check composition.

   形成性检查 书面推导

3. 03 Natural transformations 20h

   学习结果 Write a naturality square and exhibit a family of maps that fails it.

   形成性检查 反例

4. 04 Universal properties: products 20h

   学习结果 Construct a product by a unique-factorisation property in a standard category.

   形成性检查 书面推导

5. 05 Adjunctions (taught grain) 15h

   学习结果 State an adjunction by a hom-set bijection natural in both variables at synopsis grain.

   形成性检查 四选一检查

6. 06 Synthesis 15h

   学习结果 Prove a uniqueness-up-to-unique-iso claim from a universal property.

   形成性检查 书面推导

学习结果

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

学科技能

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

可迁移技能

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