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When is a variety a topos?

Algebra Universalis, 1985
Besides categories of M-sets, where M is a monoid, the categories of Jonsson-Tarski algebras seem to be the only other known examples of varieties, which are also topoi. The (binary) Jonsson-Tarski variety was first observed to be a topos by P. Freyd. This example was generalized, first by the reviewer and then by Z. Barel.
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topos

2008
Članak prikazuje genezu pojma.
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Globular perspective for Grothendieck ∞-topos and Grothendieck (∞,n)-topos

2016
In this short talk we first briefly recall how to build, for each integers n0, monads Tn on the category Glob of globular sets which algebras are globular models of (1; n)-categories, which have the virtue to be weak 1-categories of Penon and thus also to be weak 1-categories of Batanin.
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On a Topological Topos

Proceedings of the London Mathematical Society, 1979
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The Unification of Mathematics via Topos Theory

Studies in Universal Logic, 2022
Olivia Caramello
exaly  

A Topological Groupoid Representing the Topos of Presheaves on a Monoid

Applied Categorical Structures, 2020
Jens Hemelaer
exaly  

Nanocluster analysis of intermetallic structures with the program package TOPOS

Structural Chemistry, 2012
Vladislav Blatov, Blatov V A
exaly  

Topos

The Antioch Review, 1987
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Topos

1972
A. Grothendieck, J. L. Verdier
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