Give an introductory course on category theory
Get understand the universal property via adjoints, representabilities and limits.
category, functor, natural transformation, adjoint, triangle identity, universality, representability, Yoneda lemma, limit, create limit
Intercultural skills | Communication skills | ✔ Specialist skills | Critical thinking skills | Practical and/or problem-solving skills |
Give lectures on the textbook using blackboard
Course schedule | Required learning | |
---|---|---|
Class 1 | categories, functors and natural transformations | Understand the definitions of cateories, functors and natural transformations |
Class 2 | adjoints and unit/counit. | Understand the definitions of adjoints and characterization via triangle identities |
Class 3 | universalities | Understand relationships between universalities and adjoints |
Class 4 | representabilities and Yoneda lemma | Understand the definition of representabilities and representations of functors by Yoneda lemma (universal elements) |
Class 5 | limits and colimits | Understand the definitions of limits and colimits |
Class 6 | limits and functors | Understand interactions between limits and functors |
Class 7 | midterm exam | evaluate your achievement |
Class 8 | limits and representabilities | Understand relationships between limits and representabilities |
Class 9 | limits and adjoints | Understand relationships between limits and adjoints |
Class 10 | limits in functor categories | Understand behaviour of limits in functor categories |
Class 11 | adjoint functor theorem | Understand the general adjoint functor theorem and applications |
Class 12 | topos | Understand elementary toposes |
Class 13 | final exam | evaluate your achievement |
Class 14 | computer science and category theory | Explain examples of how categories are used in computer science |
Class 15 | recent topics on categorification | Explain examples of categorifications in mathematics |
Basic Category Theory, Tom Leinster, Cambridge Studies in Advanced Mathematics (avaiable at https://arxiv.org/abs/1612.09375)
I will open a lecture webpage and upload supplementing materials
based on a relative evaluation of midterm and final examinations
basic knowledge of algebra will be desirable