  Disentangling the factors of variation in data is a fundamental concept in
machine learning and has been studied in various ways by different researchers,
leading to a multitude of definitions. Despite the numerous empirical studies,
more theoretical research is needed to fully understand the defining properties
of disentanglement and how different definitions relate to each other. This
paper presents a meta-analysis of existing definitions of disentanglement,
using category theory as a unifying and rigorous framework. We propose that the
concepts of the cartesian and monoidal products should serve as the core of
disentanglement. With these core concepts, we show the similarities and crucial
differences in dealing with (i) functions, (ii) equivariant maps, (iii)
relations, and (iv) stochastic maps. Overall, our meta-analysis deepens our
understanding of disentanglement and its various formulations and can help
researchers navigate different definitions and choose the most appropriate one
for their specific context.
