In this article we prove a set of preservation properties of the reticulation functor for residuated lattices (for instance preservation of subalgebras, finite direct products, inductive limits, Boolean powers) and we transfer certain properties between bounded distributive lattices and residuated lattices through the reticulation, focusing on Stone, strongly Stone and m-Stone algebras. 2000 Ma...

Let $${\mathcal {C}}$$ be an n-angulated category. We prove that its idempotent completion $$\widetilde{{\mathcal {C}}}$$ admits a unique structure such the canonical functor $$\iota : {\mathcal {C}}\rightarrow \widetilde{{\mathcal is n-angulated. Moreover, $$ induces equivalence $$Hom _{n-ang }(\widetilde{{\mathcal {C}}},{\mathcal {D}})\cong Hom }({\mathcal {C}},{\mathcal {D}})$$ for any c...

A space $Y$ is called an {em extension} of a space $X$, if $Y$ contains $X$ as a dense subspace. Two extensions of $X$ are said to be {em equivalent}, if there is a homeomorphism between them which fixes $X$ point-wise. For two (equivalence classes of) extensions $Y$ and $Y'$ of $X$ let $Yleq Y'$, if there is a continuous function of $Y'$ into $Y$ which fixes $X$ point-wise. An extension $Y$ ...