Abstract
Abstract Is mathematical category theory a unifying tool for geography? Here we look at a few basic category theoretical ideas and interpret them in geographic example. We also offer links to indicate how category theory has been used as such in other disciplines. Finally, we announce the direction of our research program on this topic as a way to facilitate the learning, and maintenance of learning, of GIS software – and in the spirit of Quaestiones Geographicae, invite debate, comment, and contribution to this program in spatial mathematics.
Highlights
Is mathematical category theory a unifying tool for geography? Here we look at a few basic category theoretical ideas and interpret them in geographic example
Category theory is a branch of mathematics with roots in the twentieth century and development from the mid–20th century on (Eilenberg, Mac Lane 1945)
It is a language that visualizes the unity of mathematics as it economizes on thought and expression. It may expose previous unseen connections among disparate branches of mathematics. Because it is a general language, with an embedded principle of duality, a result that is proved in category theory may generate numerous results in a variety of subordinate mathematical areas
Summary
Category theory is a branch of mathematics with roots in the twentieth century and development from the mid–20th century on (Eilenberg, Mac Lane 1945). It is a language that visualizes the unity of mathematics as it economizes on thought and expression It may expose previous unseen connections among disparate branches of mathematics. A category (illustrated in Fig. 1) is composed of: –– a class of objects, –– a class of morphisms, or ”arrows”; each arrow, f, has one object as the source object of f and one object as the target object of f, –– a binary operation, ◦ , called composition of arrows, such that for any three objects, A, B, and C, the composition of f:A→B and g:B→C, is the arrow, g◦f: A→C. Too is the realization that objects and arrows might represent almost anything
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