We develop the K-theory of sets with an action a pointed monoid (or scheme), analogous to modules over ring scheme). In order form localization sequences, we construct quotient category nice regular by Serre subcategory.

Powerset structures of extensional fuzzy sets in sets with similarity relations are investigated. It is proved that extensional fuzzy sets have powerset structures which are powerset theories in the category of sets with similarity relations, and some of these powerset theories are defined also by algebraic theories (monads). Between Zadeh's fuzzy powerset theory and the classical powerset theo...

an object $x$ of a category $mathbf{c}$ with finite limits is called exponentiable if the functor $-times x:mathbf{c}rightarrow mathbf{c}$ has a right adjoint. there are many characterizations of the exponentiable  spaces in the category $mathbf{top}$ of topological spaces. here, we study the exponentiable objects in the category $mathbf{stop}$ of soft topological spaces which is a generalizati...

We study homological algebra in the abelian category Γ̃, whose objects are functors from finite pointed sets to vector spaces over Fp. The full calculation of Tor ∗ -groups between functors of degree not exceeding p is presented. We compare our calculations with known results on homology of symmetric groups, Steenrod algebra and functor homology computations in the abelian category F of functors...