Adjoints and emergence: applications of a new theory of adjoint functors |
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Authors: | David Ellerman |
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Institution: | (1) Department of Philosophy, University of California at Riverside, 4044 Mt Vernon Ave, Riverside, CA 92507, USA |
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Abstract: | 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).
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Keywords: | Adjoint functors Category theory Universal mapping properties Heteromorphisms Emergence Evolution Selectionist mechanisms Immune system Neural selectionism Generative grammar |
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