Tootfinder

No, EVE Online is not a good MMORPG alternative to Albion Online.
First of all, set in space? LOL
#NoThankYou

Podcast-Empfehlung (für starke Nerven): »Das rechte Netzwerk der Fürstin – Wie radikal ist Gloria von Thurn und Taxis?« im Radio Feature von BR2. Ich war im hinteren Drittel mehrfach kurz davor, abzubrechen. Das fürstliche Geschwurbel ist stellenweise schwer auszuhalten: ht…

The condensed homotopy type of a scheme
Peter J. Haine, Tim Holzschuh, Marcin Lara, Catrin Mair, Louis Martini, Sebastian Wolf with an appendix by Bogdan Zavyalov
https://arxiv.org/abs/2510.07443

The condensed homotopy type of a scheme
We study a condensed version of the étale homotopy type of a scheme, which refines both the usual étale homotopy type of Friedlander-Artin-Mazur and the proétale fundamental group of Bhatt-Scholze. In the first part of this paper, we prove that this condensed homotopy type satisfies descent along integral morphisms and that the expected fiber sequences hold. We also provide explicit computations, for example, for rings of continuous functions. A key ingredient in many of our arguments is a d…

Abstract Cluster Structures
Jan E. Grabowski, Sira Gratz
https://arxiv.org/abs/2510.02959 https://arxiv.org/pdf/2510.02959…

Abstract Cluster Structures
We describe a framework for encoding cluster combinatorics using categorical methods. We give a definition of an abstract cluster structure, which captures the essence of cluster mutation at a tropical level and show that cluster algebras, cluster varieties, cluster categories and surface models all have associated abstract cluster structures. For the first two classes, we also show that they can be constructed from abstract cluster structures. By defining a suitable notion of morphism of abs…