According to a result of H. Cartan (cf. [5]), the homotopy of a simplicial commutative algebra is equipped with divided power operations. In this paper, we provide a general approach to the construction of such operations in the context of simplicial algebras over an operad. To be precise, we work over a fixed field F, and we consider operads in the category of F-modules. An operad is an algebr...

Based on the monoid classifier ∆, we give an alternative axiomatization of Freyd’s paracategories, which can be interpreted in any bicategory of partial maps. Assuming furthermore a free-monoid monad T in our ambient category, and coequalisers satisfying some exactness conditions, we give an abstract envelope construction, putting paramonoids (and paracategories) in the more general context of ...

We show that there is a braided tensor category structure on the of C 1 -cofinite modules for (universal or simple) Virasoro vertex operator algebras arbitrary central charge. In generic case charge c = 13 − 6 ( t + ) , with ∉ Q we prove semisimplicity, rigidity and non-degeneracy also compute fusion rules this category.

Using techniques due to Dwyer–Greenlees–Iyengar we construct weight structures in triangulated categories generated by compact objects. We apply our result to show that, for a dg category whose homology vanishes in negative degrees and is semi-simple in degree 0, each simple module over the homology lifts to a dg module which is unique up to isomorphism in the derived category. This allows us, ...

The determination of the injective and projective members of a category is usually a challenging problem and adds to knowledge of the category. In this paper we consider these questions for the category of Heyting algebras. There has been a lack of uniformity in terminology in recent years. In [6] Heyting algebras are referred to as pseudo-Boolean algebras, and in [1] they are called Brouwerian...

lthough fuzzy set theory and  sheaf theory have been developed and studied independently,  Ulrich Hohle shows that a large part of fuzzy set  theory  is in fact a subfield of sheaf theory. Many authors have studied mathematical structures, in particular, algebraic structures, in both  categories of these generalized (multi)sets. Using Hohle's idea, we show that for a (universal) algebra $A$, th...

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...