Isomorphism of categories

The Graph Isomorphism Problem and approximate categories

It is unknown whether two graphs can be tested for isomorphism in polynomial time. A classical approach to the Graph Isomorphism Problem is the d-dimensional Weisfeiler-Lehman algorithm. The d-dimensional WL-algorithm can distinguish many pairs of graphs, but the pairs of non-isomorphic graphs constructed by Cai, Fürer and Immerman it cannot distinguish. If d is fixed, then the WL-algorithm run...

A Deligne-Riemann-Roch isomorphism I: Preliminaries on virtual categories

On Isomorphism Theorems of Fn -Polygroups

In this paper, the notion of fuzzy n-polygroups (Fn -polygroups) is introduced and some related properties are investigated. In this regards, the concepts of normal  F-subpolygroups and homomorphisms of Fn-polygroups are adopted. Also, the quotient of Fn-polygroups by defining regular relations are studied. Finally, the classical isomorphism theorems of groups are generalized to Fn-polygroups p...

A Complete Axiom System for Isomorphism of Types in Closed Categories

It is shown, that ordinary isomorphisms (associativity and commuta-tivity of tensor, isomorphisms for tensor unit and currying) provide a complete axiom system for the isomorphism of types in Symmetric Monoidal Closed categories. This gives also a decision algorithm. The problem originally arises from computer science, as the isomorphism of types in SMC categories corresponds to the isomorphism...

The Mother of All Isomorphism Conjectures via Dg Categories and Derivators

We describe a fundamental additive functor Efund on the orbit category of a group. We prove that any isomorphism conjecture valid for Efund also holds for all additive functors, like K-theory, (topological) Hochschild or cyclic homology, etc. Finally, we reduce this universal isomorphism conjecture to K-theoretic ones, at the price of introducing some coefficients.