Category theory I and foundations of mathematics [ LMAT2150 ]
5.0 crédits ECTS
45.0 h
2q
| Teacher(s) |
Vitale Enrico ;
Gran Marino ;
|
| Language |
French
|
Place
of the course |
Louvain-la-Neuve
|
| Main themes |
1) Basic examples of universal constructions : kernel, quotient group, tensor product of abelian groups, free vector space and free affine space, free group and free abelian group, abelianisation of a group, torsion free abelian groups, Cauchy completion of a metric space, logic, etc.2) Basic category theory : categories, functors, natural transformations, limits and colimits, adjoint functors, equivalences, Kan extensions.3) More examples : limits in categories of topological spaces, Tychonoff theorem, free Tychonoff space on a topological space, Stone-Cech compactification, limits in categories of Banach spaces, tensor product of rings, free K-algebra, continuum hypothesis, etc.
|
| Aims |
During the three years of BAC, several examples of universal constructions and adjoint functors have been studied. We introduce here the basic elements of category theory, whose aim is to unify and express in a rigorous way all those examples. We also try to express and solve, using categorical methods, problems coming from algebra, geometry, logic and set theory, and to recognize the categorical structure underlying the problem.
|
| Other information |
Pré-requis Néant
Evaluation Modalités à discuter entre étudiants et titulaires.
Support - F. Borceux : Handbook of categorical algebra, Cambridge University Press 1994.- S. Mac Lane : Categories for the working mathematician, Springer-Verlag 1972.
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Cycle et année
d'étude |
> Master [60] in Mathematics
> Master [120] in Mathematics
|
Faculty or entity
in charge |
> MATH
|
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