Nr. | Date | Week | Topics | Pages | |
1. | 20.01.05 | 3 | - What is Category Theory? - outline of the course | VII - XII, 1 - 11 | |
2. | 24.01.05 | 4 | - graphs and graph homomorphisms with examples - opposite graphs - path in a graph | 15 - 20 | |
3. | 27.01.05 | 4 | - definition of a category with examples: SET, GRAPH, LOGI - category of paths of a graph | 20 - 22 | |
4. | 31.01.05 | 5 | - pre-orders as categories - diagrams and commutative diagrams - isomorphisms with examples: SET, GRAPH, LOGI - isomorphic objects have the same "social life" | 22 - 28 | |
5. | 03.02.05 | 5 | - monomorphisms, epimorphisms - split monomorphisms and split epimorphisms - opposite category | 29 - 31 | |
6. | 07.02.05 | 6 | - product category - category of pointed sets, slice categories - subcategories | 32 - 38 | |
7. | 10.02.05 | 6 | - power sets, inverse image, category POWER - full and isomorphism closed subcategories - co-reflection, co-reflective subcategories: example and definiton | 38 - 40 | |
8. | 14.02.05 | 7 | - properties of co-reflective subcategories - reflection, reflective categories: definition - processes - signatures and temporal propositions | 40 - 43, 46 -47 | |
9. | 17.02.05 | 7 | - interpretation structures and satisfaction - theories and presentations, closure | 47 - 49 | |
10. | 21.02.05 | 8 | - translation maps - theory and presentation morphisms - category THEO of theories, category PRES of presentations | 50 - 52 | |
11. | 24.02.05 | 8 | - THEO as reflective and co-reflective subcategory of PRES - reducts and satisfaction condition | 52 - 55 | |
12. | 28.02.05 | 9 | - presentation lemma - institutions | 52 (131) | |
13. | 03.03.05 | 9 | - initial and terminal objects - sums with examples | 58 - 65 | |
14. | 07.03.05 | 10 | - products with examples - pushouts | 65 - 71 | |
15. | 10.03.05 | 10 | - general construction and examples of pushouts - co-equalizers - equalizers and pullbacks - general construction and examples of pullbacks | 71 - 75 | |
16. | 14.03.05 | 11 | - co-cones and colimits - cones and limits - comleteness and co-completeness - stepwise construction of limits and colimits | 75 - 81 | |
17. | 17.03.05 | 11 | - functors with examples - category CAT - special functors - preservation and reflection of isomorphisms | 83 - 88 | |
21.03.05 | 12 | no lecture | |||
24.03.05 | 12 | Maundy Thursday | |||
28.03.05 | 13 | Easter Monday | |||
31.03.05 | 13 | no lecture | |||
04.04.05 | 14 | no lecture (conference) | |||
07.04.05 | 14 | no lecture (conference) | |||
18. | 11.04.05 | 15 | - reflector (adjoint functors) - natural transformations - preservation and lifting of colimits | 88 - 92, 142 | 19. | 14.04.05 | 15 | - introduction into CommUnity - signatures and designs with examples | 177 - 182 |
20. | 18.04.05 | 16 | - interaction in Community - signature and design morphisms, categories c-SIGN and c-DSGN - functor s-sign:c-DSGN -> c-SIGN | 182 -187 | |
21. | 21.04.05 | 16 | - functor s-sign:c-DSGN -> c-SIGN as a coordinated functor - configurations and colimits: methodological discussion, examples | 188 - 190, 95, 170, - 172 | |
22. | 25.04.05 | 17 | - refinements of designs and of configurations - compositionality | 191 - 196 | |
23. | 28.04.05 | 17 | - software architecture and architectural connectors - architectural connectors in CommUnity - instantiation of connectors - special connectors | 197 - 206 | |
24. | 02.05.05 | 18 | - further special connectors Outline: - ADL-independent notion of connector - algebra of connectors - higher-order connectors | 207 - 214 | |
05.05.05 | 18 | Ascension Day | |||
25. | 09.05.05 | 17 | - course overview | ||
12.05.05 | 17 | no more lectures | |||
23.05.05 | 21 | Oral Exam | |||
24.05.05 | 21 | Oral Exam | |||