… homological properties for extriangulated categories proposed by [15]. More precisely, we
introduce the notion of the proper ξ-Gprojective resolution for any … define the functors ξxtGPpξq …

… pure submonoid, an A-parametrized persistence object in C we will mean a functor from the
… a category in their own right, where the morphisms are the natural transformations of functors…

… the obstruction classes associated with the dimension reduction of the path-integrals vanish.
In Sec. 7.3, we prove that the obstruction classes induced by a bounded-below homology …

… In §§3 and 4 we review some aspects of Hochschild homology and cohomology, which are
… Since these descriptions of the functor categories are compatible with base change along T, …

… and general linear groups but the homological algebra in F is rather mysterious. The … Now
we come back to functor categories. Let F be an indecomposable finite object in F . We can …

… among the relative extension functor, the -resolution and the Schanuel class. Furthermore,
the commonality can be used to define appropriate relative homological dimensions. …

… In this section we recall a setup for relative homological algebra in an abelian category M.
This subject, initiated by Hochschild [11], has been extensively developed in the context of the …

… that a certain homological epimorphism between two finite dimensional algebras induces
a … categories as well as between their stable categories of Gorenstein projective modules. …

… In this paper, we first introduce stable functors with respect to a complete cotorsion pair and
… As applications, we give some characterizations of objects of finite homological dimensions. …

… Finally, we observe for a functor F of the category of R-modules that the asymptotic behavior
of F(M/InM) for large n and aim … i=1 be a family of functors of the category of R-modules. Set …