Category theory may be understood as a general theory of structure. The main idea of the category-theoretic approach is to describe the properties of structures in terms of morphisms between objects, instead of the description in terms of elements and membership relations. Hence, set-theoretic notions of 'sets' or 'spaces are replaced by 'objects', while 'elements' are replaced by 'arrows' or 'morphisms".
In this way, category theory may be viewed not as a generalisation of set theory, but as an alternative foundational language which allows to describe structure in a relative way, that is, defined in terms of relations with other structures. From this perspective, the structure of every object is specified by all morphisms between this object and other objects.
(https://www.fuw.edu.pl/~kostecki/ittt.pdf)
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