INF 223, Spring 2011, Plan of Lectures

Nr. | Date | Week | Topics | Pages | |

1. | 18.01.11 | 3 | - What is Category Theory? - outline of the course | VII - XII, 1 - 11 | |

2. | 20.01.11 | 3 | - graphs and graph homomorphisms with examples - opposite graphs | 15 - 20 | |

3. | 25.01.11 | 4 | 20 - 22 | ||

4. | 27.01.11 | 4 | - path in a graph - definition of a category with examples: SET, GRAPH - category of paths of a graph | 20 - 22 | |

5. | 01.02.11 | 5 | - category LOGI and general pre-orders as categories - category MULT of sets and multi-functions - diagrams and commutative diagrams | 23 - 27 | |

6. | 03.02.11 | 5 | - isomorphisms with examples: SET, GRAPH, LOGI - isomorphic objects have the same "social life" - monomorphisms | 27 - 29 | |

7. | 08.02.11 | 6 | - epimorphisms - split monomorphisms and split epimorphisms - opposite category - duality principle - subcategories, full subcategories and discrete categories | 29 - 32 | |

8. | 10.02.11 | 6 | - discussion of "typing" - slice categories - initial objects with example in SET | 33 - 38, 58 | |

9. | 15.02.11 | 7 | - initial and terminal objects - examples in SET, LOGI, MULT - definition of sum with example in SET, LOGI and for power sets | 58 - 65 | |

10. | 17.02.11 | 7 | - sums in slice categories - definition of product with example in SET, LOGI and for inheritance - definition of pushouts and pushouts in SET - equivalence relations and quotient sets | 65 - 70 | |

11. | 22.02.11 | 8 | - pushouts in SET - pushouts by sums and co-equalizers - actualization/instantiation as pushout | 70 - 75 | |

12. | 24.02.11 | 8 | - equalizers and pullbacks - general construction and examples of pullbacks - specializations of pullback and pushout constructions | ||

13. | 01.03.11 | 9 | - co-cones and colimits - cones and limits - completeness and co-completeness | 75 - 81 | |

14. | 03.03.11 | 9 | - stepwise construction of limits and colimits - diagrams as functors - functors with examples - category CAT | ||

| 08.03.11 | 10 | no lecture (Fagkritisk dag) | ||

15. | 10.03.11 | 10 | - examples and definition of free functors - natural transformations - adjoint functors | ||

16. | 15.03.11 | 11 | |||

17. | 17.03.11 | 11 | |||

18. | 22.03.11 | 12 | |||

19. | 24.03.11 | 12 | |||

29.03.11 | 13 | no lecture (conference ETAPS) | |||

31.03.11 | 13 | no lecture (conference ETAPS) | |||

05.04.11 | 14 | ||||

07.04.11 | 14 | ||||

12.04.11 | 15 | ||||

14.04.11 | 15 | ||||

| 19.04.11 | 16 | no lecture (Easter weak) | ||

| 21.04.11 | 16 | no lecture (Easter week) | ||

26.04.11 | 17 | no lecture (Day after Easter Monday) | |||

20. | 28.04.11 | 17 | |||

21. | 03.05.11 | 18 | |||

22. | 05.05.11 | 18 | |||

23. | 10.05.11 | 19 | -course overview | ||

| 12.05.11 | 19 | No more lectures |
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22/23 | Oral Exam | ||||