These all become [T.sub.q]-[T.sub.q]-Bigalois objects [R.sub.a,b] with the left coaction
In contrast to such traditional approaches, the concept of coactive system maintains that no single system (or set of systems viewed in isolation) is primary in the production of human behavior; instead, human action and experience are emergent products of coactions
among systems that operate within and between individuals.
The ySym-Hopf module structure on PSym from Theorem 4.1 has coaction
of two antimicrobial agents can take several forms.
The NO3- production was caused by the coaction
of nitrite-oxidizing bacteria and AnAOB (anaerobic ammonium oxidationbacteria).
Definition 6 (action and coaction
of ySym on MSym) Given b [member of] M., let [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] denote a p-splitting satisfying [absolute value of [b.sub.0] > 0.
Doi-Hopf modules and Yetter-Drinfeld modules are defined as vector spaces with an action and a coaction
, with a compatibility relation that is different in both cases.
If (V, [[??].sup.V]) is a right C-comodule, then V [cross product] A is a C(A, C, [psi])-comodule with the obvious right A-multiplication and with the coaction
given as the composite
Let [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]; [V.sub.n] has a basis [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] such that the action x and the coaction
[delta] are given by