We introduce and discuss the notion of naturally full func-tor. The definition is similar to the definition of separable functor: a naturally full functor is a functorial version of a full functor, while a separable functor is a functorial version of a faithful functor. We study general properties of naturally full functors. We also discuss when func-tors between module categories and between c...

Let $R$ be a commutative ring. We write $mbox{Hom}(mu_A, nu_B)$ for the set of all fuzzy $R$-morphisms from $mu_A$ to $nu_B$, where $mu_A$ and $nu_B$ are two fuzzy $R$-modules. We make$mbox{Hom}(mu_A, nu_B)$ into fuzzy $R$-module by redefining a function $alpha:mbox{Hom}(mu_A, nu_B)longrightarrow [0,1]$. We study the properties of the functor $mbox{Hom}(mu_A,-):FRmbox{-Mod}rightarrow FRmbox{-Mo...

The purpose of this paper is the study of direct limits in category of Krasner (m, n)-hyperrings. In this regards we introduce and study direct limit of a direct system in category (m, n)-hyperrings. Also, we consider fundamental relation , as the smallest equivalence relation on an (m, n)-hyperring R such that the quotient space is an (m, n)-ring, to introdu...

This is a survey paper on the implication of Yoneda lemma, named after Japanese mathematician Nobuo Yoneda, to category theory. We prove Yoneda lemma. We use Yoneda lemma to prove that each of the notions universal morphism, universal element, and representable functor subsumes the other two. We prove that a category is anti-equivalent to the category of its representable functors as a corollar...

This paper presents an approach to the fuzzification of complete lattices. This kind of fuzzification is a functor from the category of complete lattices to the category of completeL-ordered sets. It not only can be considered as an algebraic representation of the Lowen functor ωL, but also can characterize the stratification of L-topological spaces and the underlying set of Hutton unit interval.

Let G be a finite group. It is well known that a Mackey functor {H 7→ M(H)} is a module over the Burnside ring functor {H 7→ Ω(H)}, where H ranges over the set of all subgroups of G. For a fixed homomorphism w : G → {−1, 1}, the Wall group functor {H 7→ Ln(Z[H], w|H)} is not a Mackey functor if w is nontrivial. In this paper, we show that the Wall group functor is a module over the Burnside rin...

The mirror functor as constructed by Polishchuk and Zaslow depends on various choices. This calls for a description of how the constructed functor depends on these choices. For a “good” mirror functor Φτ we would expect that we get a symplectic counterpart, that has a geometric explanation in terms of complexified symplectic tori. But unfortunately, the mirror functor does not have this expecte...