in addition to exploring constructions and properties of limits and colimits in categories of topologicalalgebras, we study special subcategories of topological algebras and their properties. in particular, undercertain conditions, reflective subcategories when paired with topological structures give rise to reflectivesubcategories and epireflective subcategories give rise to epireflective subc...

Topological materials have attracted considerable experimental and theoretical attention. They exhibit strong spin-orbit coupling both in the band structure (intrinsic) and in the impurity potentials (extrinsic), although the latter is often neglected. In this work, we discuss weak localization and antilocalization of massless Dirac fermions in topological insulators and massive Dirac fermions ...

Robertson and Seymour proved that graphs are well-quasi-ordered by the minor relation and the weak immersion relation in the prominent Graph Minors series. That is, given infinitely many graphs, one graph contains another as a minor (or a weak immersion, respectively). However, the topological minor relation does not well-quasi-order graphs. For every positive integer i, let Gi be the graph obt...

The Su-Schrieffer-Heeger . (SSH) chain is a one-dimensional lattice that comprises two dimerized sublattices. Recently, Zhu, Prodan, and Ahn (ZPA) [Phys. Rev. B 99, 041117(R) (2019)] proposed flat bands can occur at the topological domain walls of two-dimensional array SSH chains. Here, we suggest insulator protected by inversion time-reversal symmetries without spin-orbit coupling. It shown ch...