Many of the properties and aspects of nature should be understood in an inherently dynamical context. Some of them as a product or producers of dynamism, while others are to be understood as the lack of some changes that are expected to happen, as patterns of resistance to change. For this, it is pivotal to have a formal understanding of the basic unity of change, i.e., transformations. We define a transformation as a duple t = (K,s) of a set K of characteristics and a finite sequence s of entities with no constant steps, such that there is a characteristic c∈K that remains constant in each step. The concept of composition of two transformations is defined as the duple formed by the union of the sets of characteristics and the concatenation of the sequences. If we label with V the space of transformations, a subspace of V is any set S⊂V that is closed under composition of elements. Let <e> be the set of all the transformations that have e as the first element of the sequence; then, <e> is a subspace of V. It is proved that there is a category W whose set of objects is the space of entities. The set of morphisms Mor(e1,e2) is the set of transformations of e1 into e2. For every triple of entities e1, e2, and e3, a suitable restriction of the composition is the composition of morphisms between Mor(e1,e2) and Mor(e2,e3). Each identity morphism is a trivial transformation with only one step. Finally, we approach the subject of patterns of resistance to change in terms of this theory of transformations, thus refining our understanding of the wholeness and unity of nature.
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The world is a Category of transformations
Published:
04 June 2026
by MDPI
in The 2nd International Online Conference on Mathematics and Applications
session Algebra, Geometry, Topology and Logic with Applications
Abstract:
Keywords: axiomatization; analysis; category theory
