The emerging discipline of evolutionary developmental biology has opened up many new lines of investigation into morphological evolution. Here I explore how two of the core theoretical concepts in ‘evo-devo’ – modularity and homology – apply to evolutionary psychology. I distinguish three sorts of module developmental, functional and mental modules and argue that mental modules need only be ‘vi...

 Let $R=oplus_{nin Bbb N_0}R_n$ be a Noetherian homogeneous ring with local base ring $(R_0,frak{m}_0)$, $M$ and $N$ two finitely generated graded $R$-modules. Let $t$ be the least integer such that $H^t_{R_+}(M,N)$ is not minimax. We prove that $H^j_{frak{m}_0R}(H^t_{R_+}(M,N))$ is Artinian for $j=0,1$. Also, we show that if ${rm cd}(R_{+},M,N)=2$ and $tin Bbb N_0$, then $H^t_{frak{m}_0R}(H^2_...

Let R be a commutative noetherian local ring with completion b R. When R has the approximation property, we prove an approximation result for complexes with finitely generated homology. This is used to investigate descent of semidualizing complexes from b R to R. We show that, if R has the approximation property, then there is a bijective correspondence between semidualizing b R-complexes and s...

For every oriented surface of finite type, we construct a functorial Khovanov homology for links in thickening the surface, which takes values categorification corresponding gl(2) skein module. The latter is mild refinement Kauffman bracket algebra, and its constructed using category foams that admits an interesting non-negative grading. We expect natural algebra structure on module can be cate...

We identify two recursively defined polynomial conditions for FI-modules in the literature. characterize these using homological invariants of (namely local degree and regularity, together with stable degree) clarify their relationship. For one conditions, we give improved twisted stability ranges symmetric groups. As another application, improve representation congruence subgroups respect to a...