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...

In this work, using the functoriality of Drinfeld center fusion categories, we generalize full simple separable algebras in a fixed category to all categories. This generalization produces new functor, which involves both and is called pointed functor. We prove that functor symmetric monoidal equivalence. It turns out provides precise rather complete mathematical formulation boundary-bulk relat...