Related papers: Correction to "Simplicial monoids and Segal catego…
In this note we document a gap in an argument in the above paper, and point to new work in the literature giving a complete proof of the main result.
We answer Question 6.12 in the paper "Monoids in the mapping class group" written by Etnyre and Van Horn-Morris.
Monoids and groupoids are examples of poloids. On the one hand, poloids can be regarded as one-sorted categories; on the other hand, poloids can be represented by partial magmas of partial transformations. In this article, poloids are…
This contains a list of (mostly very minor) corrections to the book Introduction to Symplectic Topology, Clarendon Press, Oxford, (1995), together with rewritten versions of two lemmas and some additional comments.
We introduce and study the notion of slightly trivial extensions of a fusion category which can be viewed as the first level of complexity of extensions. We also provide two examples of slightly trivial extensions which arise from rank $3$…
We improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.
We give new, short proofs of the presentations for the partition monoid and its singular ideal originally given in the author's 2011 papers in J Alg and IJAC.
This work concerns the proof theory of (left) skew monoidal categories and their variants (e.g. closed monoidal, symmetric monoidal), continuing the line of work initiated in recent years by Uustalu et al. Skew monoidal categories are a…
We give a 3-categorical, purely formal argument explaining why on the category of Kleisli algebras for a lax monoidal monad, and dually on the category of Eilenberg-Moore algebras for an oplax monoidal monad, we always have a natural…
Minor corrections, to appear in Annali SNS.
We give a presentation of Simple Type Theory as a clausal rewrite system in Polarized deduction modulo.
These notes give an elementary approach to parts of the theory of standard Borel and analytic spaces.
In this work, we introduce the notion of a partial action of a group on a strict monoidal category. We propose, in the context of Monoidal categories, new constructions analogous to those existing for partial group actions over an algebra…
In this short note, we complete the description of low-degree characteristic classes of oriented 3-plane bundles over a 6-complex. Our goal is to point out and correct an error in L. M. Woodward's 1982 paper "The classification of principal…
A general result relating skew monoidal structures and monads is proved. This is applied to quantum categories and bialgebroids. Ordinary categories are monads in the bicategory whose morphisms are spans between sets. Quantum categories…
In this monograph, we extend S. Schwede's exact sequence interpretation of the Gerstenhaber bracket in Hochschild cohomology to certain exact and monoidal categories. Therefore we establish an explicit description of an isomorphism by A.…
These are slightly informal lecture notes intended for graduate students about the standard local theory of holomorphic foliations and vector fields. Though the material presented here is well-known some of the proofs differs slightly from…
A general theorem on fibers of singular sets is presented.
In this paper, we compare several functors which take simplicial categories or model categories to complete Segal spaces, which are particularly nice simplicial spaces which, like simplicial categories, can be considered to be models for…
Given a reductive Lie algebra over the complex numbers, we introduce a family of category which generalises the BGG category $\mathcal{O}$. We also classify the simple modules for some of these categories and prove a semisimplicity result.