Nr. | Date | Week | Topics | Pages |
1. | 19.01.06 | 3 | - What is Category Theory? - outline of the course | VII - XII, 1 - 11 |
2. | 23.01.06 | 4 | - graphs and graph homomorphisms with examples - opposite graphs - path in a graph | 15 - 20 |
3. | 26.01.06 | 4 | - definition of a category with examples: SET, GRAPH, LOGI - category of paths of a graph | 20 - 22 |
4. | 30.01.06 | 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. | 02.02.06 | 5 | - monomorphisms, epimorphisms - split monomorphisms and split epimorphisms - opposite category | 29 - 31 |
06.02.06 | 6 | no lecture | ||
6. | 09.02.06 | 6 | - product category - category of pointed sets, slice categories - subcategories | 32 - 38 |
7. | 13.02.06 | 7 | - power sets, inverse image, category POWER - full and isomorphism closed subcategories - co-reflection, co-reflective subcategories: example and definiton | 38 - 40 |
8. | 16.02.06 | 7 | - properties of co-reflective subcategories - reflection, reflective categories: definition - processes - signatures and temporal propositions | 40 - 43, 46 -47 |
9. | 20.02.06 | 8 | - interpretation structures and satisfaction - theories and presentations, closure | 47 - 49 |
10. | 23.02.06 | 8 | - translation maps - theory and presentation morphisms - category THEO of theories, category PRES of presentations | 50 - 52 |
11. | 27.02.06 | 9 | - THEO as reflective and co-reflective subcategory of PRES - reducts and satisfaction condition | 52 - 55 |
12. | 02.03.06 | 9 | - presentation lemma - institutions | 52 (131) |
13. | 06.03.06 | 10 | - initial and terminal objects - sums with examples | 58 - 65 |
14. | 09.03.06 | 10 | - products with examples - pushouts - general construction and examples of pushouts | 65 - 71 |
15. | 13.03.06 | 11 | - co-equalizers - equalizers and pullbacks - general construction and examples of pullbacks | 71 - 75 |
16. | 16.03.06 | 11 | - co-cones and colimits - cones and limits - completeness and co-completeness - stepwise construction of limits and colimits | 75 - 81 |
17. | 20.03.06 | 12 | - functors with examples - category CAT - special functors - preservation and reflection of isomorphisms | 83 - 88 |
18. | 23.03.06 | 12 | - reflector (adjoint functors) - natural transformations - preservation and lifting of colimits | 88 - 92, 142 |
27.03.06 | 13 | no lecture (conference) | ||
30.03.06 | 13 | no lecture (conference) | ||
03.04.06 | 14 | no lecture | ||
06.04.06 | 14 | no lecture (conference) | ||
10.04.06 | 15 | no lecture | ||
13.04.06 | 15 | Maundy Thursday | ||
17.04.06 | 16 | Easter Monday | ||
19. | 20.04.06 | 16 | - introduction into CommUnity - signatures and designs with examples | 177 - 182 |
20. | 24.04.06 | 17 | - interaction in Community - signature and design morphisms, categories c-SIGN and c-DSGN - functor s-sign:c-DSGN -> c-SIGN | 182 -187 |
21. | 27.04.06 | 17 | - functor s-sign:c-DSGN -> c-SIGN as a coordinated functor - configurations and colimits: methodological discussion, examples | 188 - 190, 95, 170, - 172 |
01.05.06 | 18 | May Day | ||
22. | 04.04.08 | 18 | - refinements of designs and of configurations - compositionality | 191 - 196 |
23. | 08.05.06 | 19 | - software architecture and architectural connectors - architectural connectors in CommUnity - instantiation of connectors - special connectors | 197 - 206 |
24. | 11.05.06 | 19 | - further special connectors Outline: - ADL-independent notion of connector - algebra of connectors - higher-order connectors | 207 - 214 |
25. | 15.05.06 | 20 | - course overview | |
18.05.06 | 20 | no more lectures | ||
30.05.06 | 21 | Oral Exam | ||
06.06.06 | 21 | Oral Exam | ||