Lecture notes on category theory

Definition and first examples......Page 4
Special objects and morphisms in a category......Page 7
Some constructions of categories......Page 9
Functors......Page 13
Natural transformations. Representable functors......Page 19
Yoneda's lemma......Page 24
Exercises......Page 28
(Co)products, (co)equalizers, pullbacks and pushouts......Page 30
(Co)limit of a functor. (Co)complete categories......Page 39
(Co)limits by (co)equalizers and (co)products......Page 44
(Co)limit preserving functors......Page 48
Exercises......Page 51
Definition and a generic example......Page 54
More examples and properties of adjoint functors......Page 57
The unit and counit of an adjunction......Page 60
Another characterisation of adjoint functors......Page 65
Equivalence of categories......Page 69
(Co)reflective subcategories......Page 73
Localization......Page 78
Freyd's adjoint functor theorem......Page 83
Exercises......Page 88
Bibliography......Page 89