Weak ideal topology in the topos of right acts over a monoid

Khanjanzadeh, Zeinab; Madanshekaf, Ali

doi:10.1080/00927872.2017.1360330

Cited by 5 publications

(1 citation statement)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Finally, we note that the weak Grothendieck topology induced by the left ideal I of the monoid M (as a category with just one object) associated to (⋅), which is defined as in [15] in the general case, stands for J I = {K ∈ Ω M I ⊆ K}. For a comprehensive study of weak ideal topology on the topos M-Sets we refer the reader to [19,21]. Now, we can give other examples of LT-topologies which the composition of them is not an LT-topology.…”

Section: Weak Topologymentioning

confidence: 99%

Weak Topologies on Toposes

Khanjanzadeh,

Madanshekaf

2018

Preprint

Self Cite

View full text Add to dashboard Cite

This paper deals with the notion of weak Lawvere-Tierney topology on a topos. Our motivation to study such a notion is based on the observation that the composition of two Lawvere-Tierney topologies on a topos is no longer idempotent, when seen as a closure operator. For a given topos E, in this paper we investigate some properties of this notion. Among other things, it is shown that the set of all weak Lawvere-Tierney topologies on E constitute a complete residuated lattice provided that E is (co)complete. Furthermore, when the weak Lawvere-Tierney topology on E preserves binary meets we give an explicit description of the (restricted) associated sheaf functor on E.

show abstract

Section: Weak Topologymentioning

confidence: 99%

Weak Topologies on Toposes

Khanjanzadeh,

Madanshekaf

2018

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Weak Topologies on Toposes

Khanjanzadeh

Madanshekaf

2020

Bull. Iran. Math. Soc.

View full text Add to dashboard Cite

The category 𝒮hjIMSet of sheaves in MSet

Mahmoudi

Sepahani

2022

J. Algebra Appl.

View full text Add to dashboard Cite

Since topoi were introduced, there have been efforts putting mathematics into the context of topoi. Amongst known topoi, the topoi of sheaves or presheaves over a small category are of special interest. We have here as the base topos that of sheaves over a monoid [Formula: see text] as a one object category. By means of closure operators we then obtain categories of sheaves related to the right ideals of [Formula: see text]. These categories have already been studied but we give these categories a more thorough treatment and reveal some additional properties. Namely, for a weak topology determined by a right ideal [Formula: see text] of [Formula: see text], we show that the category of sheaves associated to this topology is a subtopos of [Formula: see text] (the presheaves over [Formula: see text]) and determine the Lawvere–Tierney topology yielding the same subtopos, which is the Lawvere–Tierney topology associated to the idempotent hull of the (not necessarily idempotent) closure operator associated to [Formula: see text]. We will then find conditions under which the subcategory of separated objects turns out to be a topos, and in the last section, we find conditions under which the category of sheaves becomes a De Morgan topos.

show abstract

Weak ideal topology in the topos of right acts over a monoid

Cited by 5 publications

References 11 publications

Weak Topologies on Toposes

Weak Topologies on Toposes

Weak Topologies on Toposes

The category 𝒮hjIMSet of sheaves in MSet

Contact Info

Product

Resources

About