Ilia Pirashvili

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20112026

most citedTopos points of quasi-coherent sheaves over monoid schemes

3 citations · 8 across the 13 of their papers we have counts for

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math.CT2026

Deformation Theory of Monoid Schemes II: Precartesian Coextensions of Commutative Monoids

Ilia Pirashvili

This paper is a continuation of arXiv:2606.17088, where I studied precartesian coextensions of commutative monoids by systems of abelian groups. In this paper, we generalise it to…

math.CT2026

Deformation Theory of Monoid Schemes I

Ilia Pirashvili

The aim of this paper is to develop a deformation theory of monoid schemes, generalising the approach developed by Grillet. The core idea of this approach is to introduce the notio…

math.CT2024

Grothendieck's theory of fibred categories for monoids

Ilia Pirashvili

Grothendieck's theory of fibred categories establishes an equivalence between fibred categories and pseudo functors. It plays a major role in algebraic geometry and categorical log…

math.CT2024

On internal categories and crossed objects in the category of monoids

Ilia Pirashvili

It is a well-known fact that the category $Cat (C)$ of internal categories in a category $C$ has a description in terms of crossed modules, when $\mathbf{…

math.CT2020

Idempotents and the points of the topos of M-sets

Ilia Pirashvili

The aim of this paper is to study the points and localising subcategories of the topos of $M$ -sets, for a finite monoid $M$ . We show that the points of this topos can be fully clas…

math.CT2020

Reconstruction theorem for monoid schemes

Ilia Pirashvili

We aim to reconstruct a monoid scheme $X$ from the category of quasi-coherent sheaves over it. This is much in the vein of Gabriel's original reconstruction theorem. Under some fin…

math.CT2019★ 1 cited

On the equvialence of colimits and 2-colimits

Ilia Pirashvili

We compare the colimit and 2-colimit of strict 2-functors in the 2-category of groupoids, over a certain type of posets. These posets are of special importance, as they correspond…

math.CT2016★ 3 cited

Topos points of quasi-coherent sheaves over monoid schemes

Ilia Pirashvili

Let $X$ be a monoid scheme. We will show that the stalk at any point of $X$ defines a point of the topos $\Qc(X)$ of quasi-coherent sheaves over $X$ . As it turns out, every topos p…