This paper continues the research of the author on the homology of cubical and semi-
cubical sets with coefficients in systems. The main result is the theorem that the homology of …

The article investigates the question of under what conditions a functor between small
categories preserves cohomology groups when passing to the inverse image. For example …

We prove that a homotopy cofinal functor between small categories induces a weak
equivalence between homotopy colimits of pointed simplicial sets. This is used to prove that …

Abstract In (Xu, J Pure Appl Algebra 212: 2555–2569, 2008), a LHS-spectral sequence for
target regular extensions of small categories is constructed. We extend this construction to …

Аннотация Работа продолжает исследования автора по теории гомологий кубических
множеств с системами коэффициентов. Главный результат-доказана теорема о том …

Pointfree topology is an approach to general topology developed in the category Loc of
locales and localic maps ([1, 2]). In some respects, Loc is nicer than its classical counterpart …