We extend a result of Cisinski on the construction of cofibrantly generated model structures from (Grothendieck) toposes to locally presentable categories and from monomorphism to more general cofibrations. As in the original case, under additional conditions, the resulting model structures are ”left determined” in the sense of Rosický and Tholen.

The aim of this paper is to show several iso morphic structures between fuzzy relations and operators from the family of fuzzy sets into itself In particular we prove that the preorders family is able to embed itself in the class of fuzzy consequence operators by way of a lattice monomorphism

Let A and C be two unital simple C*-algebras with tracial rank zero. Suppose that C is amenable and satisfies the Universal Coefficient Theorem. Denote by KKe(C,A) ++ the set of those κ for which κ(K0(C)+ \ {0}) ⊂ K0(A)+ \ {0} and κ([1C ]) = [1A]. Suppose that κ ∈ KKe(C,A) . We show that there is a unital monomorphism φ : C → A such that [φ] = κ. Suppose that C is a unital AH-algebra and λ : T(...