Factorization, fibration and torsion.
Finite dimensional algebras and highest weight categories.
Finite presentation and purity in categories σ[M]
For any module M over an associative ring R, let σ[M] denote the smallest Grothendieck subcategory of Mod-R containing M. If σ[M] is locally finitely presented the notions of purity and pure injectivity are defined in σ[M]. In this paper the relationship between these notions and the corresponding notions defined in Mod-R is investigated, and the connection between the resulting Ziegler spectra is discussed. An example is given of an M such that σ[M] does not contain any non-zero finitely presented...
Finitely presentable morphisms in exact sequences.
Finitely silting comodules in quasi-finite comodule category
We introduce the notions of silting comodules and finitely silting comodules in quasi-finite category, and study some properties of them. We investigate the torsion pair and dualities which are related to finitely silting comodules, and give the equivalences among silting comodules, finitely silting comodules, tilting comodules and finitely tilting comodules.
Finiteness of the strong global dimension of radical square zero algebras
The strong global dimension of a finite dimensional algebra A is the maximum of the width of indecomposable bounded differential complexes of finite dimensional projective A-modules. We prove that the strong global dimension of a finite dimensional radical square zero algebra A over an algebraically closed field is finite if and only if A is piecewise hereditary. Moreover, we discuss results concerning the finiteness of the strong global dimension of algebras and the related problem on the density...
Finiteness Theorems for Deformations of Complexes
We consider deformations of bounded complexes of modules for a profinite group over a field of positive characteristic. We prove a finiteness theorem which provides some sufficient conditions for the versal deformation of such a complex to be represented by a complex of -modules that is strictly perfect over the associated versal deformation ring.
Flache und halbinjektive Funktoren.
Flat Modules and Torsion Theories.
Formal extension of the Whitney functor and duality
Fourier Mukai transforms and applications to string theory.
El artículo es una introducción a la transformación de Fourier-Mukai y sus aplicaciones a varios problemas de móduli, teoría de cuerdas y simetría "mirror". Se desarrollan los fundamentos necesarios para las transformaciones de Fourier-Mukai, entre ellos las categorías derivadas y los functores integrales. Se explican además sus versiones relativas, que se necesitan para precisar la noción de T-dualidad fibrada en variedades de Calabi-Yau elípticas de dimensión tres. Se consideran también varias...
Fourier-Mukai partners of canonical covers of bielliptic and Enriques surfaces
Fourier-Mukai transforms and stable bundles on elliptic curves.
Free -categories.
Free algebras and automata realizations in the language of categories
From triangulated categories to cluster algebras II
Functional separation of inductive limits and representation of presheaves by sections. Part II. Embedding of presheaves into presheaves of compact spaces
Functors on locally finitely presented additive categories