Translatability and translatable semigroups
The concept of a k-translatable groupoid is explored in depth.Some Gear Apparel properties of idempotent k-translatable groupoids, left cancellative k-translatable groupoids and left unitary k-translatablegroupoids are proved.Necessary and sufficient conditions are found for a left cancellative k-translatable groupoid to be a semigroup.Any such sem