Adjoints and emergence: applications of a new theory of adjoint functors Export

@article{citeulike:1534921, abstract = {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).}, author = {Ellerman, David}, citeulike-article-id = {1534921}, citeulike-linkout-0 = {http://dx.doi.org/10.1007/s10516-007-9008-x}, day = {28}, doi = {10.1007/s10516-007-9008-x}, journal = {Axiomathes}, keywords = {adjoint-functors, adjoints, emergence}, month = {March}, number = {1}, pages = {19--39}, posted-at = {2007-08-04 14:26:46}, priority = {2}, title = {Adjoints and emergence: applications of a new theory of adjoint functors}, url = {http://dx.doi.org/10.1007/s10516-007-9008-x}, volume = {17}, year = {2007} }

TY - JOUR ID - citeulike:1534921 L3 - citeulike-article-id:1534921 N2 - 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). IS - 1 JF - Axiomathes EP - 39 TI - Adjoints and emergence: applications of a new theory of adjoint functors VL - 17 SP - 19 KW - adjoint-functors KW - adjoints KW - emergence AU - Ellerman, David PY - 2007/03/28/ UR - http://dx.doi.org/10.1007/s10516-007-9008-x ER -