We prove two identities that connect some natural tensor products in the category $\sf{LCS}$ of locally convex spaces with $\sf{Ste}$ stereotype spaces. In particular, we give sufficient conditions under which identity $$ X^\vartriangle\odot Y^\vartriangle\cong (X^\vartriangle\cdot Y^\vartriangle)^\vartriangle\cong (X\cdot Y)^\vartriangle holds, where $\odot$ is injective product $\sf{Ste}$, $\...

We consider a family of tensor network states defined on regular lattices that come with natural definition an adiabatic path to prepare them. This comprises relevant classes states, such as injective Matrix Product and Projected Entangled-Pair States, some corresponding classical spin models. show how uniform lower bounds the gap parent Hamiltonian along trajectory can be efficiently computed ...

We develop some aspects of the homological algebra persistence modules, in both one-parameter and multi-parameter settings, considered as either sheaves or graded modules. The two theories are different. consider module sheaf tensor product Hom bifunctors well their derived functors, Tor Ext, give explicit computations for interval a classification injective, projective, flat state Kunneth theo...

In this work, we investigate measurement incompatibility in general probabilistic theories (GPTs). We show several equivalent characterizations of compatible measurements. The first is terms the positivity associated maps. second relates compatibility to inclusion certain generalized spectrahedra. For this, extend theory free spectrahedra ordered vector spaces. third characterization connects d...

we characterize function spaces of rees matrixsemigroups. then we study these spaces by using the topologicaltensor product technique.

Let G be a finite group and k be a field of characteristic p. We investigate the homotopy category K(Inj kG) of the category C(Inj kG) of complexes of injective (= projective) kG-modules. If G is a p-group, this category is equivalent to the derived category Ddg(C(BG; k)) of the cochains on the classifying space; if G is not a p-group it has better properties than this derived category. The ord...