Clustering in artificial categories: An equivalence analysis

The Special Mckay Correspondence as an Equivalence of Derived Categories

We give a new moduli construction of the minimal resolution of the singularity of type 1 r (1, a) by introducing the Special McKay quiver. To demonstrate that our construction trumps that of the G-Hilbert scheme, we show that the induced tautological line bundles freely generate the bounded derived category of coherent sheaves on X by establishing a suitable derived equivalence. This gives a mo...

An equivalence of two categories of sl(n,C)-modules

An equivalence of two categories of sl(n, C)-modules

We prove that the following two categories of sl(n,C)-modules are equivalent: 1) the category of modules with integral support filtered by submodules of Verma modules and complete with respect to Enright’s completion functor; 2) the category of all subquotients of modules F ⊗ M , where F is a finite-dimensional module and M is a fixed simple generic Gelfand-Zetlin module with integral central c...

Categories of Artificial Societies

We investigate the concept of artificial societies and identify a number of separate classes of such societies. These are compared in terms of openness, flexibility, stability, and trustfulness. The two most obvious types of artificial societies are the open societies, where there are no restrictions for joining the society, and the closed societies, where it is impossible for an “external agen...

Interleaved equivalence of categories of persistence modules

We demonstrate that an equivalence of categories using ε-interleavings as a fundamental component exists between the model of persistence modules as graded modules over a polynomial ring and the model of persistence modules as modules over the total order of the real numbers.