| Nr. | Date | Week | Topics | Pages | |
| 1. | 12.01.04 | 3 | - What is Category Theory? - outline of the course | 7 - 25 | |
| 2. | 15.01.04 | 3 | - graphs and graph homomorphisms with examples - opposite graphs | 31 - 34 | |
| 3. | 19.01.04 | 4 | - path in a graph - definition of a category with examples: SET, GRAPH | 34 - 36 | |
| 4. | 22.01.04 | 4 | - further examples of categories: LOGI, pre-orders - diagrams - isomorphisms, monomorphisms | 36 - 43 | |
| 5. | 26.01.04 | 5 | - epimorphisms - split monomorphisms and split epimorphisms - opposite category | 43 - 48 | |
| 6. | 29.01.04 | 5 | - product category - category of pointed sets, slice categories - subcategories | 48 - 54 | |
| 7. | 02.02.04 | 6 | - power sets - full and isomorphism closed subcategories - co-reflection, co-reflective subcategories | 54 - 59 | |
| 8. | 05.02.04 | 6 | - Eiffel class specifications | 59 - 62 | |
| 9. | 09.02.04 | 7 | - processes - signatures and temporal propositions - interpretation structures and satisfaction | 62 - 64 | |
| 12.02.04 | 7 | no lecture | |||
| 10. | 16.02.04 | 8 | - theories and presentations, closure - translation maps - theory and presentation morphisms - category THEO of theories, category PRES of presentations | 64 - 66 | |
| 11. | 19.02.04 | 8 | - THEO as reflective and co-reflective subcategory of PRES - reducts and satisfaction condition | 67 (71-72) | |
| 23.02.04 | 9 | no lecture | |||
| 26.02.04 | 9 | no lecture | |||
| 01.03.04 | 10 | no lecture | 12. | 04.03.04 | 10 | - presentation lemma - institutions | 67 - 69 (150) |
| 13. | 08.03.04 | 11 | - initial and terminal objects - sums with examples | 73 - 80 | |
| 14. | 11.03.04 | 11 | - products with examples - pushouts | 81 -87 | |
| 15. | 15.03.04 | 12 | - general construction and examples of pushouts - co-equalizers - equalizers and pullbacks - general construction and examples of pullbacks | 88 - 92 | |
| 16. | 18.03.04 | 12 | - co-cones and colimits - cones and limits - comleteness and co-completeness - stepwise construction of limits and colimits | 92 -98 | |
| 17. | 22.03.04 | 13 | - functors with examples - category CAT - special functors - preservation and reflection of isomorphisms | 99 - 104 | |
| 18. | 25.03.04 | 13 | - reflector (adjoint functors) - natural transformations - preservation and lifting of colimits | 104 - 109 (162) | |
| 29.03.04 | 14 | no lecture | |||
| 01.04.04 | 14 | no lecture | |||
| 05.04.04 | 15 | no lecture | |||
| 08.04.04 | 15 | no lecture | |||
| 12.04.04 | 16 | no lecture | |||
| 15.04.04 | 16 | no lecture | |||
| 19. | 19.04.04 | 17 | - introduction into CommUnity - signatures and designs with examples | 199 - 204 | |
| 20. | 22.04.04 | 17 | - interaction in Community - signature and design morphisms, categories c-SIGN and c-DSGN - functor s-sign:c-DSGN -> c-SIGN | 205 - 209 | |
| 21. | 26.04.04 | 18 | - functor s-sign:c-DSGN -> c-SIGN as a coordinated functor - configurations and colimits: methodological discussion, examples | 210 - 213 (113,192 - 194) | |
| 22. | 29.04.04 | 18 | - refinements of designs and of configurations - compositionality | 213 - 219 | |
| 23. | 03.05.04 | 19 | - software architecture and architectural connectors - architectural connectors in CommUnity - instantiation of connectors - special connectors | 221 - 232 | |
| 24. | 06.05.04 | 19 | - further special connectors Outline: - ADL-independent notion of connector - algebra of connectors - higher-order connectors | 232 - 236 | |
| 25. | 10.05.04 | 17 | - course overview | ||
| 22.04.04 | 17 | no more lectures | |||