Babes-Bolyai University of Cluj-Napoca
Faculty of Mathematics and Computer Science
Study Cycle: Graduate
SUBJECT

Code	Subject	
MA008	Theory of Categories	

Section	Semester	Hours: C+S+L	Category	Type	
Mathematics - in Romanian	7	2+2+0		optional	
Mathematics-Computer Science - in Romanian	7	2+2+0		optional	

Teaching Staff in Charge	Prof. PURDEA Ioan, Ph.D., purdea@math.ubbcluj.ro	
Aims	The study of some notions and basic results in the category theory. Using examples from other topics of algebra (studied before), it will be characterized in the terms of some universal properties of the main constructions in mathematics and the natural aspect of certain connections between them.	
Content	Necessity of axiomatization of Set Theory, elements of Godel-Bernays axiomatic theory. 
Category and subcategory. Duality principle. Special morphisms in a category. 
Special objects in a category. Subobjects and quotient objects. Kernels and cokernels. 
Normal subobjects and conormal quotient objects. Exact categories. Products and coproducts. Semiadditive, additive and abelian categories. Functors. Natural transformations.	
Bibliography	1. PURDEA I., Tratat de algebra moderna, Vol.II, Ed. Acad., 1982.
2. HERRILICH H., STRECKER G.E., Category theory, Boston, 1973.
3. POPESCU N., Categorii abeliene, Ed. Acad., 1971.
4. POPESCU N., POPESCU L., Theory of categories, Ed. Acad., 1979.
5. MACLANE S., Categories for the working mathematician, New York, 1965.
6. MITCHELL B. Theory of categories, Pure and Applied Mathematics, Vol. XVII, Academic Press, New York-London, 1965.
	
Assessment	Tests (50% x final grade). Exam (50% x final grade).