Related papers: Correction to "Simplicial monoids and Segal catego…
This is a corrected version of my paper published in Journal of Geometry and Physics 25(1998), 205-226. I added missing cases to the classification theorem 1.1, namely the $SO(n+1)$-manifold $SO(n +2)/ (SO (n) \times SO(2))$, the…
In this paper, we state and prove precise theorems on the classification of the category of (braided) categorical groups and their (braided) monoidal functors, and some applications obtained from the basic studies on monoidal functors…
We obtain simple proofs of certain inequalites for bivariate means.
We answer a question raised in ``Peripheral elements in reduced Alexander modules'' [J. Knot Theory Ramifications 31 (2022), 2250058]. We also correct a minor error in that paper.
In this paper, we classify finite categories with two objects such that one of the endomorphism monoids is a group. We prove that having a group on one side affects the structure of the other endomorphism monoid, and we prove that it is…
The main purpose of this paper is to introduce the structure of soft group category. In this category, we determine some special objects and morphisms having a universal structure such as the final object and product. Therefore, the…
The article presents a complete classification of $n$-valued monoids and groups of order 3. Important corollaries of this result are discussed.
The note corrects the aforementioned paper (also, arXiv:0902.4716). The consequences of the correction are traced and the examples updated.
There are some inaccuracies and errors in my article "Dual and almost-dual homogeneous spaces". Here I will describe in detail how to correct incorrect statements from this article and which statements there will have to be reformulated in…
Our published paper contains an incorrect statement of a result due to Artin and Zhang. This corrigendum gives the correct statement of their result and includes a new result that allows us to use their result to prove our main theorem.…
In this paper we study grouplike monoids, these are monoids that contain a group to which we add an ordered set of idempotents. We classify finite categories with two objects having grouplike endomorphism monoids, and we give a count of…
These notes cover background material on trees which are used in the paper `On uniqueness of the signature of a path of variation and the reduced path group'.
This note corrects one serious mistake and several smaller mistakes from arXiv:math/0502404. The main results of that paper are unchanged.
We correct the proofs of the main theorems in our paper "Limit theorems for Betti numbers of random simplicial complexes".
These are notes for a graduate-level introductory course on singularity categories.
In these notes we provide the foundation for the deformation theoretic parts of arXiv:0807.3753 and arXiv:math/0102005.
We use a theory of colax Reedy diagrams to show that the category of Segal M-precategories with fixed set of objects has a model structure for a symmetric monoidal model category M = (M,\otimes,I). What is relevant here is when M is…
In \cite{LS14} the analogy between the Kleisli construction and the construction of "warping a skew monoidale category" in the sense of \cite{LS12} was outlined. In this note we present the same work in a slightly more formal way.
These are notes from a basic course in Several Complex Variables
Although multiplier bimonoids in general are not known to correspond to comonoids in any monoidal category, we classify them in terms of maps from the Catalan simplicial set to another suitable simplicial set; thus they can be regarded as…