A general framework for cluster tilting is set up by showing that any quotient of a triangulated category modulo a tilting subcategory (that is, a maximal oneorthogonal subcategory) carries an induced abelian structure. These abelian quotients turn out to be module categories of Gorenstein algebras of dimension at most one.

We prove that in an abelian category with enough projective objects, the extension subcategory of two covariantly finite subcategories is still covariantly finite. This extends a result by Sikko and Smalø. We also prove a triangulated version of the result. As applications, we obtain short proofs to a classical result by Ringel and a recent result by Krause and Solberg. 1. Main Theorems Let C b...

My principal references are [Serre:1965], [Reutenauer:1993], and [de Graaf:2000]. My interest in free Lie algebras has been motivated by the well known conjecture that Kac-Moody algebras can be defined by generators and relations analogous to those introduced by Serre for finite-dimensional semi-simple Lie algebras. I have had this idea for a long time, but it was coming across the short note [...

1. Yang-Baxter algebras (YBA), introduced in [1, 2, 3], generalize the wideknown FRT construction [4] in the following sense: to any numerical matrix solution R of the Yang-Baxter equation there is associated a bialgebra containing the FRT one as a sub-bialgebra. Generally, this construction may provide examples of (new) bialgebras and Hopf algebras [5]. In several aspects, there is some simila...

In this article we will build a universal imbedding of a regular HomLie triple system into a Lie algebra and show that the category of regular Hom-Lie triple systems is equivalent to a full subcategory of pairs of Z2graded Lie algebras and Lie algebra automorphism, then finally give some characterizations of this subcategory.

We put cluster tilting in a general framework by showing that any quotient of a triangulated category modulo a tilting subcategory (that is, a maximal one-orthogonal subcategory) carries an induced abelian structure. These abelian quotients turn out to be module categories of Gorenstein algebras of dimension at most one.

A general framework for cluster tilting is set up by showing that any quotient of a triangulated category modulo a tilting subcategory (that is, a maximal oneorthogonal subcategory) carries an induced abelian structure. These abelian quotients turn out to be module categories of Gorenstein algebras of dimension at most one.

Several methods for constructing left determined model structures are expounded. The starting point is Olschok’s work on locally presentable categories. We give sufficient conditions to obtain left determined model structures on a full reflective subcategory, on a full coreflective subcategory and on a comma category. An application is given by constructing a left determined model structure on ...

In this paper, we investigate the L-fuzzy proximities and the relationships betweenL-fuzzy topologies, L-fuzzy topogenous order and L-fuzzy uniformity. First, we show that the category of-fuzzy topological spaces can be embedded in the category of L-fuzzy quasi-proximity spaces as a coreective full subcategory. Second, we show that the category of L -fuzzy proximity spaces is isomorphic to the ...