in this article, we have shown, for the add-point monad t, thepartial morphism category set*is isomorphic to the kleisli category sett. alsowe have proved that the category, sett, of t-algebras is isomorphic to thecategory set of pointed sets. finally we have established commutative squaresinvolving these categories.

MV-algebras were introduced by Chang as an algebraic counterpart of the Lukasiewicz infinite-valued logic. D. Mundici proved that the category of MV-algebras is equivalent to the category of abelian l-groups with strong unit. A. Di Nola and A. Lettieri established a categorical equivalence between the category of perfect MV-algebras and the category of abelian l-groups. In this paper we investi...

The paper is devoted to a concept of a fuzzy ordered set and partially ordered set category fuzzyfication. The aim of this work is to define a fuzzy order relation on a usual set, on an L-valued set and on an L-set. Using the fuzzy order relation we construct fuzzy POS category and study the connection between this categories and SET(L).

We fix a base field k of characteristic not dividing l. We suppose that k contains a primitive l-th root of unity ζ , and fix it. Starting from these data, one defines certain category C. Its objects are finite dimensional X-graded k-vector spaces equipped with an action of Lusztig’s ”small” quantum group u (cf. [L2]) such that the action of its Cartan subalgebra is compatible with the X-gradin...

The present paper is primarily concerned with the study of L-guilds in an L-merotopic space. It is shown that every L-cluster is an L-guild; however the converse is not true. For contigual and regular L-merotopies, where on one side we gave an example of a space, which is neither contigual nor binary, on the other side we constructed L-merotopic spaces that are contigual and binary. It is shown...

In SGA 4 [1], one of the principal building blocks of the theory of topoi is Giraud’s theorem, which says that the condition of a 1-category A being the category of sheaves on a site, may be characterized by intrinsic, internal conditions in A. The intrinsic conditions are basically existence of certain limits and colimits, plus a condition about generation by a small set of objects. In this pa...

In previous work [7], the authors constructed and studied a lift of the Galois correspondence to stable homotopy categories. In particular, if L/k is a nite Galois extension of elds with Galois group G, there is a functor c∗ L/k : SHG → SHk from the G-equivariant stable homotopy category to the stable motivic homotopy category over k such that c∗ L/k (G/H+) = Spec(L)+. The main theorem of [7] s...

in this paper, let $l$ be a completeresiduated lattice, and let {bf set} denote the category of setsand mappings, $lf$-{bf pos} denote the category of $lf$-posets and$lf$-monotone mappings, and $lf$-{bf cslat}$(sqcup)$, $lf$-{bfcslat}$(sqcap)$ denote the category of $lf$-completelattices and $lf$-join-preserving mappings and the category of$lf$-complete lattices and $lf$-meet-preserving mapping...