| Nr. | Date | Week | Topics | Pages | |
| 1. | 15.01.07 | 3 | - What is Category Theory? - outline of the course | VII - XII, 1 - 11 | |
| 2. | 17.01.07 | 3 | - graphs and graph homomorphisms with examples - opposite graphs - path in a graph | 15 - 20 | |
| 3. | 22.01.07 | 4 | - definition of a category with examples: SET, GRAPH - category of paths of a graph | 20 - 22 | |
| 4. | 24.01.07 | 4 | - pre-orders as categories - diagrams and commutative diagrams - isomorphisms with examples: SET, GRAPH - isomorphic objects have the same "social life" | 22 - 28 | |
| 5. | 29.01.07 | 5 | - monomorphisms, epimorphisms - split monomorphisms and split epimorphisms - opposite category | 29 - 31 | |
| 6. | 31.01.07 | 5 | - category of pointed sets, slice categories - subcategories | 32 - 38 | |
| 7. | 05.02.07 | 6 | - power sets, inverse image, category POWER - full and isomorphism closed subcategories - co-reflection, co-reflective subcategories: example and definiton | 38 - 40 | |
| 8. | 07.02.07 | 6 | - properties of co-reflective subcategories - reflection, reflective categories: definition | 40 - 43 | |
| 9. | 12.02.07 | 7 | - processes - signatures and temporal propositions - interpretation structures and satisfaction - theories and presentations, closure | 46 - 49 | |
| 10. | 14.02.07 | 7 | - translation maps - theory and presentation morphisms - category THEO of theories, category PRES of presentations | 50 - 52 | |
| 19.02.07 | 8 | no lecture (conference) | 52 - 55 | ||
| 21.02.07 | 8 | no lecture (conference) | |||
| 11. | 26.02.07 | 9 | - THEO as reflective and co-reflective subcategory of PRES - reducts and satisfaction condition | 52 - 55 | |
| 12. | 28.02.07 | 9 | - presentation lemma - institutions | 52 (131) | |
| 13. | 05.03.07 | 10 | - initial and terminal objects - sums with examples | 58 - 65 | |
| 14. | 07.03.07 | 10 | - products with examples - pushouts - general construction and examples of pushouts | 65 - 71 | |
| 15. | 12.03.07 | 11 | - co-equalizers - equalizers and pullbacks - general construction and examples of pullbacks | 71 - 75 | |
| 16. | 14.03.07 | 11 | - co-cones and colimits - cones and limits - comleteness and co-completeness | 75 - 81 | |
| 17. | 19.03.07 | 12 | - stepwise construction of limits and colimits - specializations of pullback and pushout constructions | 83 - 88 | |
| 18. | 21.03.07 | 12 | - diagrams as functors - functors with examples - category CAT - natural transformations | 88 - 92, 142 | |
| 26.03.07 | 13 | no lecture (conference) | |||
| 28.03.07 | 13 | no lecture (conference) | |||
| 02.04.07 | 14 | no lecture (conference) | |||
| 04.04.07 | 14 | no lecture (conference) | |||
| 09.04.07 | 15 | Easter Monday | |||
| 11.04.07 | 15 | no lecture (Student meeting) | |||
| 19. | 16.04.07 | 16 | - diagrammatic specifications - definition of sketches with examples | ||
| 20. | 17.04.07 | 16 | - sketch morphisms - set-theoretical models of sketches - examples of semantical universe - SET, PAR, MULTI - sketching diagrammatic techniques - general scheme - sketching ER-diagrams and class diagrams | ||
| 21. | 23.04.07 | 17 | - dependencies - sketch operations | ||
| 22. | 24.04.07 | 17 | - idea of (meta-)modeling - model vs. instance - valid instances - idea of Grothendieck construction | ||
| 30.04.07 | 18 | no lecture (May Day) | |||
| 01.05.07 | 18 | no lecture (May Day) | |||
| 23. | 07.05.07 | 19 | - functor category - Grothendieck construction | ||
| 08.05.07 | 19 | no lecture | |||
| 24. | 14.05.07 | 20 | - model transformation - course overview | ||
| 15.05.07 | 20 | no more lectures | |||
| 23/24 | Oral Exam | ||||