Closedness properties of internal relations
and approximate operations
Zurab Janelidze
I will give a brief overview of the work done regarding closedness properties of
internal relations, which were introduced in my MSc Thesis, and regarding
approximate operations which D. Bourn and I have recently introduced. Closedness
properties of internal relations provide a tool for translating universal algebraic term
conditions into purely categorical conditions. Approximate operations enhance this
tool and also allow to make a next step: it becomes possible to extend theorems for
classes of varieties defined by term conditions, to theorems for classes of categories
defined by the corresponding categorical conditions.