Functorially Finite Subcategories

In this thesis,we prove the following results for subcategories of an exact category:1)The full subcategory of extensions of objects from two contravari-antly finite subcategories L and B is contravariantly finite,provided that there are enough injective objects.2)The full subcategory whose objects are cokernel-s of maps between two covariantly finite subcategories E and B is covariantly finite,provided that there are enough projective objects and E is a cogenerating subcategory.Similarly,we prove the following results for subcategories of a triangulated category:1)The full subcategory whose objects are weak kernels of maps be-tween two contravariantly finite subcategories Y and L is contravariantly finite.2)The full subcategory of extensions of objects from two contravariantly finite subcategories X and L is contravariantly finite.3)The full subcategory whose objects are weak cokernels of maps between two contravariantly finite subcate-gories X and Y is contravariantly finite.Finally,the above results are generalized to extriangulated categories,that is,we prove the following results for subcategories:1)The full subcategory of extensions of objects from strongly covariantly finite subcategory E and covari-antly finite subcategory B is covariantly finite,provided that there are enough projective objects.2)The full subcategory whose objects are cocones of maps between two strongly contravariantly finite subcategories F and B is strongly contravariantly finite,provided that there are enough injective objects.