This paper is concerned with two problems which, although not apparently closely related, are solved in part by the same methods. The first problem is: given a bicomplete (=comple te and cocomplete) category X and a triple T on X, is X T also bicomplete? The second is: given a category X and a functor R: X---~X, does R generate a free triple? This paper began as an attempt to show that the cate...

Talk 1: Big Goal of Alg Top, operads and model categories, fix notation for model categories, remarks about how difficult it is to verify model category axioms. Motivation from equivariant spectra, and discussion of Kervaire. Monoidal model categories, define the inherited model structure on the category of algebras over an operad. Basic facts about Bousfield localization. Preservation theorem ...

In the work of Hoshino, Kato andMiyachi, [11], the authors look at t-structures induced by a compact object, C, of a triangulated category, T , which is rigid in the sense of Iyama and Yoshino, [12]. Hoshino, Kato and Miyachi show that such an object yields a non-degenerate t-structure on T whose heart is equivalent to Mod(End(C)). Rigid objects in a triangulated category can the thought of as ...

We develop a symmetric analog of brace algebras and discuss the relation of such algebras to L∞-algebras. We give an alternate proof that the category of symmetric brace algebras is isomorphic to the category of pre-Lie algebras. As an application, symmetric braces are used to describe transfers of strongly homotopy structures. We then explain how these symmetric brace algebras may be used to e...

We develop a symmetric analog of brace algebras and discuss the relation of such algebras to L∞-algebras. We give an alternate proof that the category of symmetric brace algebras is isomorphic to the category of pre-Lie algebras. As an application, symmetric braces are used to describe transfers of strongly homotopy structures. We then explain how these symmetric brace algebras may be used to e...

In this note, we introduce the concept of a fuzzy filter of a BLalgebra,with respect to a t-norm briefly, T-fuzzy filters, and give some relatedresults. In particular, we prove Representation Theorem in BL-algebras. Thenwe generalize the notion of a fuzzy congruence (in a BL-algebra) was definedby Lianzhen et al. to a new fuzzy congruence, specially with respect to a tnorm.We prove that there i...

The paper studies the interrelationship between coverings of finite directed graphs and gradings of the path algebras associated to the directed graphs. To include gradings of all basic finite-dimensional algebras over an algebraically closed field, a theory of coverings of graphs with relations is introduced. The object of this paper is to relate group gradings on algebras to coverings of a gr...

In this paper we investigate effective descent morphisms in categories of reflexive and transitive lax algebras. We show in particular that open and proper maps are effective descent, result that extends the corresponding results for the category of topological spaces and continuous maps. Introduction A morphism p : E → B in a category C with pullbacks is called effective descent if it allows a...

We present a general framework for logics of transition systems based on Stone duality. Transition systems are modelled as coalgebras for a functor T on a category X . The propositional logic used to reason about state spaces from X is modelled by the Stone dual A of X (e.g. if X is Stone spaces then A is Boolean algebras and the propositional logic is the classical one). In order to obtain a m...