Since the inception of the notion of fuzzy topology much attention was paid to the possible means of interaction between fuzzy and crisp topological settings, in order to see whether fuzzy topology was doing anything new. In particular, different functors relating the categories Top of topological spaces and L-Top of Ltopological spaces (L being a suitable complete lattice) appeared in the lite...

We study a connection between mapping spaces of bimodules and infinitesimal over an operad. As main application motivation our work, we produce explicit delooping the manifold calculus tower associated to space smooth maps D m → n $D^m\rightarrow D^n$ discs, ⩾ $n\geqslant m$ , avoiding any given multisingularity coinciding with standard inclusion near boundary ∂ $\partial D^m$ . In particular, ...

Recently, a new category of domains used for the mathematical foundations of denotational semantics, that of L-domains, have been under study. In this paper we consider a related category of posets, that of local lattices. First, a completion operator taking posets to local lattices is developed, and then this operator is extended to a functor from posets with embedding-projection pairs to loca...

semi-regular locales are extensions of the classical semiregularspaces. we investigate the conditions such that semi-regularizationis a functor. we also investigate the conditions such that semi-regularizationis a reflection or coreflection.

In this paper, we consider the forgetful functor from the category LDcpo of local dcpos (respectively, Dcpo of dcpos) to the category Pos of posets (respectively, LDcpo of local dcpos), and study the existence of its left and right adjoints. Moreover, we give the concrete forms of free and cofree S-ldcpos over a local dcpo, where S is a local dcpo monoid. The main results are: (1) The forgetful...

For every profinite group G, we construct two covariant functors ∆G and APG from the category of commutative rings with identity to itself, and show that indeed they are equivalent to the functor WG introduced in [A. Dress and C. Siebeneicher, The Burnside ring of profinite groups and the Witt vectors construction, Adv. Math. 70 (1988), 87-132]. We call ∆G the generalized Burnside-Grothendieck ...

The Euler–Koszul complex is the fundamental tool in the homological study of A-hypergeometric differential systems and functions. We compare Euler–Koszul homology with D-module direct images from the torus to the base space through orbits in the corresponding toric variety. Our approach generalizes a result by Gel’fand et al. [GKZ90, Thm. 4.6] and yields a simpler, more algebraic proof. In the ...