| Nr. | Date | Week | Topics | Pages | |
| 1. | 16.01.18 | 3 | - What is Category Theory? - shift of paradigm - informal discussion of products, dualization, sums | 5 - 8 | |
| 2. | 18.01.18 | 3 | - graphs and graph homomorphisms: motivation, examples, definition - opposite graphs - discussion of isomorhisms between graphs | 8 - 12 | |
| 3. | 23.01.18 | 4 | - composition of maps and identity maps - composition of graph homomorphisms and identity graph homomorphisms - associativity and identity law of composition - definition of category | 12 - 14 | |
| 4. | 25.01.18 | 4 | - categories Set and Graph - a universal definition of isomorphism - composition of isomorphisms is isomorphism - isomorphisms in Set are bijective maps - some finite categories - representation of finite categories by pictorial diagrams | 14 - 16 | |
| 5. | 30.01.18 | 5 | - other categories with sets as objects: Incl, Inj, Par - subcategory: examples and definition - Nat and Incl as pre-order categories - discussion associations in class diagrams - composition of relations | 17 - 22 | |
| 6. | 01.02.18 | 5 | - category Rel - association ends and multimaps - category Mult - monoids: examples and definition | 23 - 27 | |
| 7. | 06.02.18 | 6 | - monoid morphisms: examples and definition - category Mon of monoids - universal property of lists - functors: motivation, definition | 27 - 29 | |
| 8. | 08.02.18 | 6 | - functors: examples - product categories - opposite category and contravariant functors - identity functors and composition of functors - categories of categories: Cat, CAT, SET, GRAPH | 29 - 32 | |
| 9. | 13.02.18 | 7 | - pathes: motivation, examples, definition - path graph and evaluation of paths - categorical diagrams: motivation, definition, examples - commutative diagram: definition and examples - path categories - summary of the first lectures about "structures" | 32 - 33 | |
| 10. | 15.02.18 | 7 | - general discussion about models and metamodels - discussion of a "metamodel" MG of graphs - graphs as interpretations of the graph MG in Set - graph homomorphisms as natural transformations - definition of natural transformations - natural transformations: composition and identities - definition of interpretation categories - indexed sets as functor category - arrow categories - category of E-graphs | 35 - 39 | |
| 11. | 20.02.18 | 8 | - discussion of arrows between arrows - path equations, satisfaction of path equations - model interpretations - reflexive graphs - motivation of "typing" by ER-diagrams and Petri nets - type graph and typed graphs and their morphisms | 39 - 42 | |
| 12. | 22.02.18 | 8 | - definition slice category - example typed E-graphs - indexed vs. typed sets - equivalence of categories - equivalence relations and equivalence classes - quotient sets and natural maps - unique factorization of maps | 43 - 48 | |
| 13. | 27.02.18 | 9 | - equivalences as abstraction in mathematics - representatives and normal forms - quotient path categories - monomorphisms: definition, examples in Set, Graph, Incl | 48 - 56 | |
| 14. | 01.03.18 | 9 | no lecture (illness) | 56 - 60 | |
| 15. | 06.03.18 | 10 | - epimorphisms: definition, examples in Set, Graph, Incl - split mono's and epi's - in Set all epi's are split -> axiom of choice - initial objects: definition, examples in , Incl, Set, , Mult, Graph - terminal objects: definition, examples in , Incl, Set, Mult, Graph | ||
| 08.03.18 | 10 | - sum: definition, examples in , Incl, Set, Graph - product: definition, examples in , Incl, Set, Graph | |||
| 16. | 13.03.18 | 11 | - motivation pullbacks: intersection, inner join, products of typed graphs - pullbacks: definition, examples in Incl, Set, Graph - preimages as pullbacks - equalizers: definition, example in Set - kernel and graph of a map f:A->B as equalizers | ||
| 17. | 15.03.18 | 11 | - general construction of pullbacks by products and equalizers - fibred products - equalizers are mono - monics are reflected by pullbacks, coding of monics by pullbacks - composition of pullbacks is a pullback and decomposition of pullbacks | ||
| 18. | 20.03.18 | 12 | - motivation pushouts: sharing, decomposition of graphs, rule applications - pushouts: definition, examples in , Incl, Set, Graph - coequalizers, general construction of pushouts by sums and coequalizers - discussion: two lines of constructions | ||
| 19. | 22.03.18 | 12 | - definition of diagrams - cones and limits - co-cones and colimits - completeness and co-completeness - stepwise construction of limits and colimits | ||
| 27.03.18 | 13 | no lecture (Easter Holiday) | |||
| 29.03.18 | 13 | no lecture (Maundy Thursday) | |||
| 03.04.18 | 14 | no lecture (conference) | |||
| 05.04.18 | 14 | Additional: lecture about monads | |||
| 20. | 10.04.18 | 15 | - research project: flexible and universal diagrammatic formalism - categorical sketches: example binary relations - criticism of sketch approach | ||
| 21. | 12.04.18 | 15 | - relation = jointly injective/monic - dualization = jointly surjective/epic (cover), example subclasses - ER diagrams in DPF - key = injective map - composite attributes = products - formalization of associations: predicate [opp] | ||
| 22. | 17.04.18 | 16 | - diagrammatic signature: definition and examples - atomic constraints - diagrammatic specification - discussion of two variants of EER models - semantic interpretations in a "semantic universe" U - indexed semantics = interpretation categories - satisfaction of atomic constraints - specification morphisms: definition and example; category of specifications | ||
| 23. | 19.04.18 | 16 | - revised type graph for ER diagrams - semantics-as-instances - discussion extending type graphs to metamodels - informal discussion of modelling hierarchies | ||
| 24. | 24.04.18 | 17 | - typed signatures, typed atomic constraints, typed specifications - conformant specification - modelling formalism and modelling hierarchies | ||
| 26.04.18 | 17 | no lecture (institute seminar) | |||
| 01.05.18 | 18 | no lecture (Labor Day) | |||
| 25. | 03.05.18 | 18 | - discussion model transformation - joined modelling formalism - example object-oriented models joined with relational data models - transformation rules: definition - model transformation = application of transformation rule = pushout - example from oo models to relational data models - discussion control of rule applications: negative application conditions, stratification - discussion: extracting the constructed relational data model by pullback | ||
| 26. | 08.05.18 | 19 | - course summary | ||
| 10.05.18 | 19 | no lecture ( Ascension Day) | |||
| 20 | No more lectures | ||||
| 21 | No more lectures | ||||
| 22 | No more lectures | ||||
| 04.06.15 | 23 | Oral Exam | |||