The early ideas of a universal language with complete conceptual classification by categories is still debated on various levels.
Using the current terminology, it would have taken five years to end up with a complete classification, 50% of which would be already obsolete.
There is a complete classification of three-dimensional lens spaces, by fundamental group and Reidemeister torsion.
A complete classification of homogeneous distributions in one dimension is possible.
Today we have a complete classification of hyperfinite factors.
Mathematicians often strive for a complete classification (or list) of a mathematical notion.
A complete classification of 1D gapped quantum phases (with interactions)
For neurotmesis, it is better to use a new more complete classification called the Sunderland System.
Several authors have provided additional conditions that classify some graphs as being of class one or class two, but do not provide a complete classification.
This paper gives a complete classification of simple and semisimple algebras.