a ≤ b iff a is the supremum of the subset {a} ∩ {b}. On any elementary topos E , one has the functor which to an object A associates the object TA = Ã which classifies partial maps into A (cf e.g. [J] 1.2). This functor T carries a monad structure T= (T, η, μ) ; it is a submonad of the power ”set” monad P= (P, η, μ), as described in, say, [AL],[Mi], or [J] 5.3. We shall analyze the category of ...

The main goal of the paper is a description connected and projective objects classes categories that include acts along with pointed acts. In order to establish general context unify approach both acts, notion concrete category unique decomposition introduced studied. Although these are not extensive in general, it proved they satisfy version extensivity which ensures every noninitial object un...

By constructing Hopf costructures on closure spaces via homotopy, we give the concepts of cospace (CH-cospace) and cogroup (CH-cogroup). We then prove that retract deformation a CH-cospace are also CH-cospace. construct costructure set with help quotient operator. show space same homotopy type as CH-cogroup is itself CH-cogroup. existence covariant functor between category pointed ($\mathcal{CH...

We present a comparative study of certain invariants defined for group actions and their analogues orbifolds. In particular, we prove that Fadell's equivariant category $G$-spaces coincides with the Lusternik-Schnirelmann orbifolds when is finite.