We formulate a categorical mechanism by which boundary-layer dynamics emerges from mixed Yoneda obstructions in a Fukaya-type category. Let F FF be a smooth proper A∞A_∞-category equipped with two competing autoequivalences Φ1, Φ2₁, ₂Φ1, Φ2 whose logarithmic growth rates are distinct. Under the Yoneda embedding, an object L∈FL FL∈F is represented by its Floer response module Y (L) =HomF (−, L) Y (L) =Hom ₅ (-, L) Y (L) =HomF (−, L). When the two autoequivalence sectors fail to align simultaneously, the Yoneda module decomposes into two pure components and a residual mixed component Ymix (L) Y ₌₈ₗ (L) Ymix (L). We interpret this residual component as a mixed Yoneda obstruction. The non-vanishing of this obstruction defines a categorical boundary layer. On this boundary layer, the mismatch between continuous transport and discrete autoequivalence action induces an obstruction curvature and a natural quadratic defect functional. The Hessian of this defect functional provides an effective stiffness for a collective boundary-layer coordinate. When the two sectoral growth rates are unequal, the mixed coordinate drifts, causing the collective mode to acquire a time-dependent effective frequency. The resulting equation is a Hill-type parametric oscillator. This construction gives a purely categorical route from autoequivalence asymmetry to Floquet dynamics. As an application, a positive Floquet exponent may be interpreted as an emergent effective expansion rate, yielding an effective dark-energy sector without inserting a bare cosmological constant. The symmetric limit, in which the two growth rates coincide, removes the mixed drift and collapses the effective sector. The framework is therefore best viewed not as a complete cosmological model, but as a categorical mechanism for producing small effective residuals from obstruction dynamics.
Jeong Min Yeon (Sat,) studied this question.