De student:
* is bekend met de basisprincipes van de categorie-theorie
* kent een groot aantal voorbeelden van categorieen en functoren
* is in staat om in nieuwe categorieen de grondbegrippen zelfstandig toe te passen
* is bekend met modulen over ringen
* is in staat de structuur van modulen over bepaalde type ringen (zoals hoofdideaalringen) te analyseren
* is in staat om zelfstandig te werken met vrije resoluties
* is bekend met de basisprincipes van de homologische algebra
* kan eenvoudige berekeningen doen met complexen, homotopieen van complexen en de berekening van afgeleide functoren
|
|
In this course we will give a first introduction to category theory, aimed at mathematicians. This provides us with a uniform langage that is useful to analyse _structures_ regardless of in which branch of maths they appear. As such it is an indispensible tool for further study of pure maths.
In parallel with this we will develop some Algebra, notably the theory of modules over rings. This is of great independent interest but also serves to illustrate many of the categorical notions that we will see.
The two strands are interwoven in the second half of the course, when we will give a first introduction to homological algebra. Here begins a mathematical development that has shaped much mathematics since the 1950s and today is an indispensible tool in many branches of maths.
|
|
|
|
|
|