Axiomathes 17 (1):19-39 (2007)

David Ellerman
University of Ljubljana
Since its formal definition over sixty years ago, category theory has been increasingly recognized as having a foundational role in mathematics. It provides the conceptual lens to isolate and characterize the structures with importance and universality in mathematics. The notion of an adjunction (a pair of adjoint functors) has moved to center-stage as the principal lens. The central feature of an adjunction is what might be called “determination through universals” based on universal mapping properties. A recently developed “heteromorphic” theory about adjoints suggests a conceptual structure, albeit abstract and atemporal, for how new relatively autonomous behavior can emerge within a system obeying certain laws. The focus here is on applications in the life sciences (e.g., selectionist mechanisms) and human sciences (e.g., the generative grammar view of language).
Keywords Adjoint functors  Category theory  Universal mapping properties  Heteromorphisms  Emergence  Evolution  Selectionist mechanisms  Immune system  Neural selectionism  Generative grammar
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DOI 10.1007/s10516-007-9008-x
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Darwin's Dangerous Idea: Evolution and the Meanings of Life.David L. Hull - 1997 - British Journal for the Philosophy of Science 48 (3):435-438.
Darwin's Dangerous Idea: Evolution and the Meanings of Life.Daniel C. Dennett - 1995 - American Journal of Theology and Philosophy 17 (2):235-240.

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On Adjoint and Brain Functors.David Ellerman - 2016 - Axiomathes 26 (1):41-61.

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