INF 223, Spring 2005, Plan of Lectures






Nr.DateWeekTopicsPages





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





14.07.03.0510 - products with examples
- pushouts
65 - 71
15.10.03.0510 - general construction and examples of pushouts
- co-equalizers
- equalizers and pullbacks
- general construction and examples of pullbacks
71 - 75





16.14.03.0511 - co-cones and colimits
- cones and limits
- comleteness and co-completeness
- stepwise construction of limits and colimits
75 - 81
17.17.03.0511 - functors with examples
- category CAT
- special functors
- preservation and reflection of isomorphisms
83 - 88





21.03.0512 no lecture
24.03.0512 Maundy Thursday





28.03.0513 Easter Monday
31.03.0513 no lecture





04.04.0514 no lecture (conference)
07.04.0514 no lecture (conference)





18.11.04.0515 - reflector (adjoint functors)
- natural transformations
- preservation and lifting of colimits
88 - 92, 142
19.14.04.0515 - introduction into CommUnity
- signatures and designs with examples
177 - 182





20.18.04.0516 - interaction in Community
- signature and design morphisms, categories c-SIGN and c-DSGN
- functor s-sign:c-DSGN -> c-SIGN
182 -187
21.21.04.0516 - functor s-sign:c-DSGN -> c-SIGN as a coordinated functor
- configurations and colimits: methodological discussion, examples
188 - 190, 95, 170, - 172





22.25.04.0517 - refinements of designs and of configurations
- compositionality
191 - 196
23.28.04.0517 - software architecture and architectural connectors
- architectural connectors in CommUnity
- instantiation of connectors
- special connectors
197 - 206





24.02.05.0518 - further special connectors
Outline:
- ADL-independent notion of connector
- algebra of connectors
- higher-order connectors
207 - 214
05.05.0518 Ascension Day





25.09.05.0517 - course overview
12.05.0517 no more lectures










23.05.0521 Oral Exam
24.05.0521 Oral Exam