Floquet phases of matter have attracted great attention due to their dynamical and topological nature that are unique nonequilibrium settings. In this work, we introduce a generic way taking any integer q q th-root the evolution operator U display="inline">U describe...

This paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. It incorporates the most important settings of lattice-valued topology, including poslat topology of S.~E.~Rodabaugh, $(L,M)$-fuzzy topology of T.~Kubiak and A.~v{S}ostak, and $M$-fuzzy topology on $L$-fuzzy sets of C.~Guido. Moreover, its respe...