Faculty of Mathematics and Computer Science

Theory of categories |

Code |
Semes-ter |
Hours: C+S+L |
Credits |
Type |
Section |

Teaching Staff in Charge |

Prof. PURDEA Ioan, Ph.D., purdea@math.ubbcluj.ro |

Aims |

The study of notions and basic results in the theory of categories. Using examples from other algebraic subjects studied before, it will be emphasized the characterization by universality properties of the main constructions in mathematics and the natural aspect of certain connections of theirs. |

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 ransformations. |

References |

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. |

Assessment |

Exam. |