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Ganea term for CCG-homology of crossed modules.

Teimuraz Pirashvili (2000)

Extracta Mathematicae

In [2] an internal homology theory of crossed modules was defined (CCG-homology for short), which is very much related to the homology of the classifying spaces of crossed modules ([5]). The goal of this note is to construct a low-dimensional homology exact sequence corresponding to a central extension of crossed modules, which is quite similar to the one constructed in [3] for group homology.

Generalized canonical algebras and standard stable tubes

Andrzej Skowroński (2001)

Colloquium Mathematicae

We introduce a new wide class of finite-dimensional algebras which admit families of standard stable tubes (in the sense of Ringel [17]). In particular, we prove that there are many algebras of arbitrary nonzero (finite or infinite) global dimension whose Auslander-Reiten quivers admit faithful standard stable tubes.

G-functors, G-posets and homotopy decompositions of G-spaces

Stefan Jackowski, Jolanta Słomińska (2001)

Fundamenta Mathematicae

We describe a unifying approach to a variety of homotopy decompositions of classifying spaces, mainly of finite groups. For a group G acting on a poset W and an isotropy presheaf d:W → (G) we construct a natural G-map h o c o l i m d G / d ( - ) → | W | which is a (non-equivariant) homotopy equivalence, hence h o c o l i m d E G × G F d → E G × G | W | is a homotopy equivalence. Different choices of G-posets and isotropy presheaves on them lead to homotopy decompositions of classifying spaces. We analyze higher limits over the categories associated to isotropy presheaves...

Gorenstein projective complexes with respect to cotorsion pairs

Renyu Zhao, Pengju Ma (2019)

Czechoslovak Mathematical Journal

Let ( 𝒜 , ℬ ) be a complete and hereditary cotorsion pair in the category of left R -modules. In this paper, the so-called Gorenstein projective complexes with respect to the cotorsion pair ( 𝒜 , ℬ ) are introduced. We show that these complexes are just the complexes of Gorenstein projective modules with respect to the cotorsion pair ( 𝒜 , ℬ ) . As an application, we prove that both the Gorenstein projective modules with respect to cotorsion pairs and the Gorenstein projective complexes with respect to cotorsion pairs possess...

Gorenstein star modules and Gorenstein tilting modules

Peiyu Zhang (2021)

Czechoslovak Mathematical Journal

We introduce the notion of Gorenstein star modules and obtain some properties and a characterization of them. We mainly give the relationship between n -Gorenstein star modules and n -Gorenstein tilting modules, see L. Yan, W. Li, B. Ouyang (2016), and a new characterization of n -Gorenstein tilting modules.

Graph Cohomology, Colored Posets and Homological Algebra in Functor Categories

Jolanta Słomińska (2012)

Bulletin of the Polish Academy of Sciences. Mathematics

The homology theory of colored posets, defined by B. Everitt and P. Turner, is generalized. Two graph categories are defined and Khovanov type graph cohomology are interpreted as Ext* groups in functor categories associated to these categories. The connection, described by J. H. Przytycki, between the Hochschild homology of an algebra and the graph cohomology, defined for the same algebra and a cyclic graph, is explained from the point of view of homological algebra in functor categories.

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