  The transition towards data-centric AI requires revisiting data notions from
mathematical and implementational standpoints to obtain unified data-centric
machine learning packages. Towards this end, this work proposes unifying
principles offered by categorical and cochain notions of data, and discusses
the importance of these principles in data-centric AI transition. In the
categorical notion, data is viewed as a mathematical structure that we act upon
via morphisms to preserve this structure. As for cochain notion, data can be
viewed as a function defined in a discrete domain of interest and acted upon
via operators. While these notions are almost orthogonal, they provide a
unifying definition to view data, ultimately impacting the way machine learning
packages are developed, implemented, and utilized by practitioners.
