Context: In this study, we embrace information by presenting important concepts of abstract information field theory, probabilities, and probabilistic dimensions, in the view of functors of actions theories and other abstract theories. Methodology: The methods used are the presentation of a collection of manifold-metric pairs, probabilistic notions, simple topology, and Einstein-Boltzman equations and the combination of this collection. Results: These combinations result to different flavours of an expanding sub-manifold and metric systems describing simpler dynamics of space around massive objects. Furthermore, we derive the equation of motion of a simplified gravity model in a probabilistic expanding Universe. We further introduce the notions of probabilistic actions and concepts of novel categories of abstract field-particles, such as the probablons and informatons. Conclusion: We conclude that the derived equations are the first steps towards a concrete description of a probabilistic gravity, and a probabilistic expanding Universe descriptions.

In this document we describe the novel concept of generalisation of tensor. We expand the concepts expressed in previous studies by considering the generalisation of the tensor concept. We introduce the generalised index of a tensor, an index describing several types of indices of a tensor. Furthermore, we describe the connection between category theory and tensor calculus. In particular, we explore the concepts of functor tensor, or functorial tensor, tensor with categories as elements. This work opens new avenues to mathematical analysis, tensor analysis, tensor theory, and category theory.

In this document, we review the basics of category theory and functors calculus, and we implement some novel concepts. In particular, we review the concepts of category, functors, and natural transformations. Furthermore we introduce the novel concept of func- tors of functors. We illustrate these concepts with diagrams to ameliorate the expression of these ideas. We conclude that these concepts open new avenues and are advancing category.