Related papers: Categorical rings subsume ann-categories

The paper has been withdrawn.

The automorphism groups of certain factorial complex affine threefolds admitting locally trivial actions of the additive group are determined. As a consequence new counterexamples to a generalized cancellation problem are obtained.

Algorithmic recourse provides explanations that help users overturn an unfavorable decision by a machine learning system. But so far very little attention has been paid to whether providing recourse is beneficial or not. We introduce an…

The paper has been withdrawn for further elaboration.

We extend the notion of regular coherence from rings to additive categories and show that well-known consequences of regular coherence for rings also apply to additive categories. For instance the negative K-groups and all twisted…

Cluster algebras are categorified by cluster categories, and $g$-vectors are categorified by the classic index with respect to cluster tilting subcategories. However, the recently introduced completed discrete cluster categories of Dynkin…

This paper was withdrawn by the authors. Lemma 5.1 is wrong.

This paper has been withdrawn because the models on which it was based have undergone significant changes and improvements. A new paper with the same title, based on the improved models, is accepted for publication in MNRAS and is available…

A commutative ring is reduced when it can be embedded into a direct product of fields. While the category of reduced commutative rings plays a fundamental role in affine geometry, it exhibits several structural deficiencies: it admits…

The paper is withdrawn. The proof has an error and it requires a different approach.

This paper has been withdrawn by the authors; it will be incorporated into part I of the series (in preparation).

This paper has been withdrawn because the content has been substantially improved in a later paper, arXiv:0806.1165.

For any cssc-crossed module a category is constructed, equipped with a structure and proved that this is a coherent categorical group. Together with a result of the previous paper, where to any categorical group the cssc-crossed module is…

This paper has been withdrawn by the authors due to crucial error in the main proof (located in Section 2.4). The authors apologize for any inconveniences.

This paper has been withdrawn by the author due to an error in Lemma 3, making the (bijective) proof of Theorem 4 and Corollary 5 invalid (symmetry of k-nonnesting and k-noncrossing set partitions).

This paper has been withdrawn by the author due to the paper does not belong to Condensed Matter field.

This paper has been withdrawn

This paper has been withdrawn by the author, since one of the key results duplicates existing work, as pointed out by a reader. I am currently revising the manuscript.

This paper has been withdrawn by the author. Much simpler proof of the main result was obtained which led to major changes in the presentation.

This paper has been withdrawn by the author for further investigation.