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FOUNDATIONS OF MATHEMATICS (530SM)

A.A. 2019 / 2020

Periodo 
Secondo semestre
Crediti 
6
Durata 
48
Tipo attività formativa 
Caratterizzante
Percorso 
[PDS0-2018 - Ord. 2018] comune
Syllabus 
Lingua insegnamento 

English

Obiettivi formativi 

KNOWLEDGE AND UNDERSTANDING
By the end of the course the student is expected to be familiar with the category language and algebraic categories, including limits and adjoint functors.
CAPACITY TO APPLY KNOWLEDGE AND UNDERSTANDING
By the end of the course the student is expected to be able to apply the notions of category theory acquired to solve problems and exercises of medium difficulty. The exercises can also be proposed as easy theoretical results.

Prerequisiti 

Algebra basic courses

Contenuti 

Advanced topics in algebra and in depth study of some research issues about:
- Category language
- Limits
- Adjoint functors
- Algebraic categories

Metodi didattici 

Lectures and exercises. The solutions will be discussed in class with the students.

Programma esteso 

Advanced topics in algebra and in depth study of some research issues about:
- Category language
- Limits
- Adjoint functors
- Algebraic categories

Modalità di verifica dell'apprendimento 

The exam program coincides with the arguments of the lectures.
The final oral test consists in verifying the comprehension of the contents (definitions and proofs) and in the ability in explaining and elaborating the subject.

Altre informazioni 

Some lectures will be given in joint presence, as a coteacher, with prof. Marino Gran (Université Catholique de Louvain).

Testi di riferimento 

S. MAC LANE : Categorie nella pratica matematica.
H. HERRLICH - G. STRECKER : Category Theory.
H. SCHUBERT : Categories
F. BORCEUX : Handbook of categorical algebra I e II
M. BARR- C. WELLS : Category Theory for computing Science


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