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Action Preserving (Weak) Topologies on the Category of Presheaves by Khanjanzadeh, Zeinab; Madanshekaf, Ali is a scholarly article available to read on EtoBox.

What is Action Preserving (Weak) Topologies on the Category of Presheaves about?

Let $\mathcal{C}$ be a finitely complete small category. In this paper, first we construct two weak (Lawvere-Tierney) topologies on the category of presheaves. One of them is established by means of a subfunctor of the Yoneda functor and the other one, is constructed by an admissible class on $\mathcal{C}$ and the internal existential quantifier in the presheaf topos $\widehat{\mathcal{C}}$. Moreover, by using an admissible class on $\mathcal{C},$ we are able to define an action on the subobject classifier $\Omega$ of $\widehat{\mathcal{C}}$. Then we find some necessary conditions for that the two weak topologies and also the double negation topology $\neg\neg$ on $\widehat{\mathcal{C}}$ to be action preserving maps. Finally, among other things, we constitute an action preserving weak topology on $\widehat{\mathcal{C}}$.

Author

Khanjanzadeh, Zeinab; Madanshekaf, Ali

Published

2017

Language

EN