Regular CA-Groupoids and Cyclic Associative Neutrosophic Extended Triplet Groupoids (CA-NET-Groupoids) with Green Relations

n-groupoids and stacky groupoids

We discuss two generalizations of Lie groupoids. One consists of Lie n-groupoids defined as simplicial manifolds with trivial πk≥n+1. The other consists of stacky Lie groupoids G ⇒ M with G a differentiable stack. We build a 1–1 correspondence between Lie 2-groupoids and stacky Lie groupoids up to a certain Morita equivalence. We prove this in a general set-up so that the statement is valid in ...

Linearization of Regular Proper Groupoids

Let G be a Lie groupoid over M such that the target-source map from G to M ×M is proper. We show that, if O is an orbit of finite type (i.e. which admits a proper function with finitely many critical points), then the restriction G|U of G to some neighborhood U of O in M is isomorphic to a similar restriction of the action groupoid for the linear action of the transitive groupoid G|O on the nor...

Finite idempotent groupoids and regular languages

0 Foliation groupoids and their cyclic homology ∗

Congruence Relations on Hypergroupoids and Nd-groupoids

In this work we prove that the set of congruences on an nd-groupoid under suitable conditions is a complete lattice which is a sublattice of the lattice of equivalence relations on the nd-groupoid. The study of these conditions allowed to construct a counterexample to the statement that the set of (fuzzy) congruences on a hypergroupoid is a complete lattice.