Related papers: Correction to "Simplicial monoids and Segal catego…

We give a criterion of the semisimplicity of a p-adic unitary representation of a topological monoid by the reduction of the associated operator algebra.

We make two tiny corrections to our previous paper with the same title, and also obtain, as a bonus, something new.

This paper has been withdrawn, because I have merged it with paper I of the series, math.AG/0312190. The main results of this paper now appear in sections 7-9 of the revised version of math.AG/0312190, with shortened and improved proofs.

This thesis is devoted to the proof of a theorem showing the existence of a closed model category structure for weakly enriched categories. It requires first of all the definitions of weakly enriched categories and equivalences of weakly…

We follow the work of Aguiar on internal categories and introduce simplicial objects internal to a monoidal category as certain colax monoidal functors. Then we compare three approaches to equipping them with a discrete set of vertices. We…

This paper has been withdrawn by the author; see the much expanded, improved, and generalized version at arXiv:0811.2073.

We prove a structure result on proper extensions of two-sided restriction semigroups in terms of partial actions, generalizing respective results for monoids and for inverse semigroups and upgrading the latter. We introduce and study…

It is shown that the category of \emph{semi-biproducts} of monoids is equivalent to the category of \emph{pseudo-actions}. A semi-biproduct of monoids is a new notion, obtained through generalizing a biproduct of commutative monoids. By…

Some sufficient conditions on a simplicial space $X$ guaranteeing that $X_1\simeq \Omega|X|$ were given by Segal. We give a generalization of this result for multisimplicial spaces. This generalization is appropriate for the reduced bar…

This is the last part of a series of three strongly related papers in which three equivalent structures are studied: - internal categories in categories of monoids; defined in terms of pullbacks relative to a chosen class of spans - crossed…

We give an overview of the parts of arXiv:2004.04279 that deal with 2-categories, up to and including adjunction, and explain how the Segal-type approach to 2-categories adopted there is related to the more standard approaches. As an…

In this note, we use certain sesquilinear form to realize small theta lift for even orthogonal-symplectic and unitary dual pairs over p-adic fields.

The purpose of this short note is to present a simplified proof of Serre's modularity conjecture using the strong modularity lifting results currently available. This second version includes extra details on definitions and proofs than the…

This paper introduces a skew variant of the notion of enriched category, suitable for enrichment over a skew-monoidal category, the main novelty of which is that the elements of the enriched hom-objects need not be in bijection with the…

This paper is a corrigendum to the article 'Some notes on the classification of shift spaces: Shifts of Finite Type; Sofic Shifts; and Finitely Defined Shifts'. In this article we correct Lemma 5.3. Therefore, we follow correcting…

In a step towards the classification of endotrivial modules for quasi-simple groups, we investigate endotrivial modules for the sporadic simple groups and their covers. A main outcome of our study is the existence of torsion endotrivial…

The bicategory of normal functors between W*-categories is monoidally equivalent to the bicategory of W*-bimodules.

We offer two proofs that categories weakly enriched over symmetric monoidal categories can be strictified to categories enriched in permutative categories. This is a "many 0-cells" version of the strictification of bimonoidal categories to…

We introduce a new type of weakly enriched categories over a given symmetric monoidal model category M; these are called Co-Segal categories. Their definition derives from the philosophy of classical (enriched) Segal categories. We study…

We modify the proof of the basic lemma of a paper of Saks and Zygmund on additive functions of rectangles.