Related papers: Categorical rings subsume ann-categories
This paper has been withdrawn by the author(s), due a crucial sign error in Thm. 11.
This paper has been withdrawn by the authors due to essential errors in Theorem 5.6.
This paper has been withdrawn
This paper has been withdrawn by the author, due to a crucial error in the proof of Lemma 3.1.
The results of this thesis allows one to replace calculations in tricategories with equivalent calculations in Gray categories (aka semistrict tricategories). In particular the rewriting calculus for Gray categories as used for example by…
In a 2006 article Schlichting conjectured that the negative {\it K--}theory of any abelian category must vanish. This conjecture was generalized in a 2019 article by Antieau, Gepner and Heller, who hypothesized that the negative {\it…
This paper was withdrawn by the author. It turns out that similar ideas have been presented before. The author apologizes.
This paper was withdrawn as it may have appeared elsewhere, although in a different form.
We construct recursion categories from categories of coalgebras. Let $F$ be a nontrivial endofunctor on the category of sets that weakly preserves pullbacks and such that the category $\textbf{Set}_F$ of $F$-coalgebras is complete. The…
This submission has been withdrawn at the request of the author.
A braided $Ann$-category $\mathcal A$ is an $Ann$-category $\mathcal A$ together with a braiding $c$ such that $(\mathcal A, \otimes, a, c, (1,l,r))$ is a braided tensor category, moreover $c$ is compatible with the distributivity…
We focus on working on incidence rings, a class of (possibly infinite) matrix rings indexed by ordered sets. Some general properties about them are given, including how they are always the inverse limit of finite matrix rings, giving a…
This paper has been withdrawn by the authors due to an error in Section 7.
This paper has been withdrawn.
The paper is withdrawn. The reviewer pointed out that the assertion that the quantity $D_{\Gamma}$ is finite (used by the author) is still unproved for the general group, and perhaps is false.
The paper is withdrawn by the authors and replaced be an improved and extended version arxiv: 0812.2968
A recent Comment [arXiv:0811.2790] on the Letter 'Quantum Bounce and Cosmic Recall' by the authors is shown to arise from an incorrect understanding of the issues at hand and of our analysis. The conclusions of Bojowald's Comment are shown…
We withdraw this paper due to insufficient arguments in the derivation of Theorem 1. See quant-ph/0005062 for the new paper
We show that if two rings have equivalent derived categories then they have the same algebraic K-theory. Similar results are given for G-theory, and for a large class of abelian categories.
This paper presents the proof of the coherence theorem for Ann-categories whose set of axioms and original basic properties were given in [9]. Let $$\A=(\A,{\Ah},c,(0,g,d),a,(1,l,r),{\Lh},{\Rh})$$ be an Ann-category. The coherence theorem…