Probing L-S category with maps

A radical extension of the category of $S$-sets

Let S-Set be the category of $S$-sets, sets together with the actions of a semigroup $S$ on them. And, let S-Pos be the category of $S$-posets, posets together with the actions compatible with the orders on them. In this paper we show that the category S-Pos is a radical extension of S-Set; that is there is a radical on the category S-Pos, the order desolator radical, whose torsion-free class i...

COGENERATOR AND SUBDIRECTLY IRREDUCIBLE IN THE CATEGORY OF S-POSETS

In this paper we study the notions of cogenerator and subdirectlyirreducible in the category of S-poset. First we give somenecessary and sufficient conditions for a cogenerator $S$-posets.Then we see that under some conditions, regular injectivityimplies generator and cogenerator. Recalling Birkhoff'sRepresentation Theorem for algebra, we study subdirectlyirreducible S-posets and give this theo...

(r,t)-injectivity in the category $S$-Act

In this paper, we show that injectivity with respect to the class $mathcal{D}$  of dense monomorphisms of an idempotent and weakly hereditary closure operator of an arbitrary category  well-behaves. Indeed, if $mathcal{M}$ is a subclass of monomorphisms, $mathcal{M}cap mathcal{D}$-injectivity  well-behaves. We also introduce the notion of $(r,t)$-injectivity in the category {bf S-Act}, where $r...

“Spaces over a Category and Assembly Maps in Isomorphism Conjectures in K-and L-Theory” by

We give a unified approach to the Isomorphism Conjecture of Farrell and Jones on the algebraic Kand L-theory of integral group rings and to the Baum-Connes Conjecture on the topological K-theory of reduced group C∗-algebras. The approach is through spectra over the orbit category of a discrete group G. We give several points of view on the assembly map for a family of subgroups and describe suc...

The L 2 geometry of spaces of harmonic maps S 2 → S