“Lecture Category theory”

Consider the following question: \[ \text{Why category theory? It is abstract nonsense and completely useless, right?} \] Well, there are many views and reasons to study category theory, and here is a short and biased list:


Daniel Tubbenhauer email

Please put [Lecture Category theory] as the subject.


Where and when?


  1. 21.Feb.2022, Speaker: Daniel Tubbenhauer, Topic: The beginnings - What is...category theory?
  2. 28.Feb.2022 Speaker: Daniel Tubbenhauer, Topic: Diagrams in categories - Commuting and alike
  3. 07.Mar.2022, Speaker: Daniel Tubbenhauer, Topic: Functors I - The basics about functors
  4. 14.Mar.2022, Speaker: Daniel Tubbenhauer, Topic: Functors II - Natural transformations and equivalence
  5. 21.Mar.2022, Speaker: Daniel Tubbenhauer, Topic: Yoneda - Yoneda lemma and Yoneda embedding
  6. 28.Mar.2022, Speaker: Daniel Tubbenhauer, Topic: Limits I - Examples of limits
  7. 04.Apr.2022, Speaker: Daniel Tubbenhauer, Topic: Limits II - Universal properties and limits abstractly
  8. 11.Apr.2022, Speaker: Daniel Tubbenhauer, Topic: Adjoint functors I - The algebraic approach
  9. 18.Apr.2022, Speaker: Daniel Tubbenhauer, Topic: Adjoint functors II - The diagrammatic approach
  10. 25.Apr.2022, Speaker: Daniel Tubbenhauer, Topic: Monoids I - Monads and their modules
  11. 02.May.2022, Speaker: Daniel Tubbenhauer, Topic: Monoids II - Monoidal categories
  12. 09.May.2022, Speaker: Daniel Tubbenhauer, Topic: Whats next? - Some outlook including diagrammatics


The exercises correspond 1:1 to the talks in the list above.
  1. 21.Feb.2022, Exercise 1, Click
  2. 28.Feb.2022, Exercise 2, Click
  3. 07.Mar.2022, Exercise 3, Click
  4. 14.Mar.2022, Exercise 4, Click
  5. 21.Mar.2022, Exercise 5, Click
  6. 28.Mar.2022, Exercise 6, Click
  7. 04.Apr.2022, Exercise 7, Click
  8. 11.Apr.2022, Exercise 8, Click
  9. 18.Apr.2022, Exercise 9, Click
  10. 25.Apr.2022, Exercise 10, Click
  11. 02.May.2022, Exercise 11, Click
  12. 09.May.2022, Exercise 12, Click


Here are a few references used in this lecture:
  1. [AL91] A. Asperti, G. Longo. Categories, types, and structures. An introduction to category theory for the working computer scientist. Foundations of Computing Series. MIT Press, Cambridge, MA, 1991.
  2. [AHS90] J. Adámek, H. Herrlich, G.E. Strecker. Abstract and concrete categories: the joy of cats. Reprint of the 1990 original [Wiley, New York; MR1051419]. Repr. Theory Appl. Categ. No. 17 (2006), 1-507. URL: Click
  3. [BL11] J.C.Baez, A.D.Lauda. A prehistory of $n$-categorical physics. Deep beauty, 13-128. Cambridge Univ. Press, Cambridge, 2011. URL: Click
  4. [FS19] B.Fong, D.I.Spivak. An invitation to applied category theory. Seven sketches in compositionality. Cambridge University Press, Cambridge, 2019. xii+338 pp. URL: Click
  5. [La17] E.Landry et al. Categories for the working philosopher. Edited by Elaine Landry. Oxford University Press, Oxford, 2017. xiv+471 pp.
  6. [Le14] T.Leinster. Basic category theory. Cambridge Studies in Advanced Mathematics, 143. Cambridge University Press, Cambridge, 2014. viii+183 pp. URL: Click
  7. [ML98] S.Mac Lane. Categories for the working mathematician. Second edition. Graduate Texts in Mathematics, 5. Springer-Verlag, New York, 1998. xii+314 pp.
  8. [Mi14] B.Milewski. Category Theory for Programmers. Collected from the series of blog posts. URL: Click. URL: Click
  9. [Ri16] E.Riehl. Category Theory in Context. Dover Publications, 2016. URL: Click
  10. [Si11] H.Simmons. An introduction to category theory. Cambridge University Press, Cambridge, 2011. x+226 pp.