Body, Category of Sets, Category Theory, Concept, Conceptual Mathematics, Element, Example, Figure, Function, Locus, Map Object, Mathematical Concept, Mathematics, Object, One, Organization, Philosophy, Property, Set, Singleton Set, Size, Sorting, Structure, Terminal Object, Textbook, Understanding, Universal Mapping Property, Value, Varying Element
Body of mathematical concepts
Mathematical concepts such as 1, singleton set, and objects satisfying universal mapping properties are placed in well-defined positions. One ready illustration: the way 1 is related to a singleton set (property-value of a structure) is determinately definite and different from the ways in which singletons are related to objects satisfying universal mapping properties (example, sorting). We can also, for example, read vividly going from 1 to singleton set to terminal object to objects satisfying universal mapping properties to map object to its size–a number–all in the space of a line segment: a figure is the locus of a varying element (Conceptual Mathematics, page 83). Mathematical concepts, from this perspective, appear to be clearly organized.
Would you be kind enough to point me to our current understanding (say, a textbook) of the structure of the body of mathematical concepts.
Happy Philosophy Day!