Courses – Fakultet tehničkih nauka u Novom Sadu

Subject: Categorial proof theory (17.DOM45L)

Type of studies	Title
Doctoral Academic Studies	Mathematics in Engineering (Year: 1, Semester: Summer)

General information:

Category	Scientific-professional
Scientific or art field	Applied Computer Science and Informatics Teorijska i primenjena matematika
ECTS	10

The student has to acquire fundamental knowledge about Categorial proof theory with a particular focus on results of coherence for various categories of interest for classical propositional logic. Participating in scientific and research work.

Knowledge about fundamental notions and results in category theory. Students included into research activities in some areas of category theory and proof theory in collaboration with national or international research teams.

Fundamental results in proof theory, basic notions in category theory, basic notions in categorial proof theory: Introduction to coherence and categorification, Syntactical categories and basic notions in category theory, Monoidal categories, Symmetrical monoidal categories, Bimonoidal categories, Dissociative categories, Bicartesian categories, Distributive bicartesian categories, Categories with zero morphisms, Boolean categories.

The presentation of the theoretical part during the lectures is followed by the characteristic examples which contribute to better understanding of the subject matter. The students are expected to individually study the additional literature which they discuss with the subject teacher at the consultation classes. Through research and study work the student will, on the bases of scientific journals and other relevant literature that has been studied independently, develop further understanding of the material covered in lectures. Working with the course teacher the student develops the ability to independently work on a scientific paper.

Authors	Title	Year	Publisher	Language
Mac Lane, S.	Categories for the Working Mathematician	1998	Springer, New York	English
G.Gentzen	Investigations into logical deduction	1969	North-Holand, Amsterdam	English
K. Došen, Z. Petrić	Proof-Theoretical Coherence	2004	KCL Publications London	English
Lambek, J., Scott, P.J.	Introduction to Higher Order Categorical Logic	1994	Camgridge University Press, Cambridge	English