Related papers: Birational geometry and localisation of categories
In these self-contained low prerequisite introductory notes we first present (in part 1) basic concepts of set theory and algebra without explicit category theory. We then present (in part 2) basic category theory involving a somewhat…
This very short correction notes a gap in an argument of an earlier paper, and also provides a theorem of similar flavor to the main result of that paper.
This paper has been withdrawn, because its material has been revised and became part of paper math.GT/0010184
There is an error in the proof of Proposition 3.7. Proposition 3.7 is needed for the proof of the main theorem.
Misprints in eq. (7), which propagate up to eq. (13), are corrected. References are updated.
This paper has been withdrawn by the author, due to a counter example to step 6.2 indicated by K. Karu.
The familiar construction of categories of fractions, due to Gabriel and Zisman, allows one to invert a class W of arrows in a category in a universal way. Similarly, bicategories of fractions allow one to invert a collection of arrows in a…
This note corrects conditions in Proposition 3.4 and Theorem 5.2(ii) and comments on imprecisions in Propositions 4.2 and 4.4 in Fissler and Ziegel (2016).
In this article we introduce the notion of a square structure on a model category, that generalises cubical model categories. We then show that under some homotopical conditions on this square structure the induced cubical category is a…
We fill in a gap in the proof of the main theorem in our earlier paper [Ol]. At the same time, we prove a slightly stronger version of the theorem needed for another paper.
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.
This note points out a gap in the proof of the main theorem of the article "Birationally rigid hypersurfaces" published in Invent. Math. 192 (2013), 533-566, and provides a new proof of the theorem.
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…
This paper corrects a small mistake in a paper of Dwyer-Kan, and uses this to identify homotopy function complexes in a model category with the nerves of certain categories of zig-zags.
We correct some oversights in the paper "A spectral sequence for stratified spaces and configuration spaces of points" by the second named author. In particular we explain that an additional hypothesis should be added to Theorem 4.15 in…
The aim of this note is to give a quick algebraic proof of (the combinatorial part of) the classification theorem for compact real surfaces, whose classical proofs (as in the Massey book and in the Conway ZIP proof) are based on surgery…
This paper contains corrections to Madea, Rosenberg, Torres-Ardila, "The Geometry of Loop Spaces II: Characteristic Classes," Advances in Math. (287), 2016, 485-518. The main change is that results about $\pi_1({\rm Diff}(M))$ are replaced…
We define a 2-category structure (Pre-Orb) on the category of reduced complex orbifold atlases. We construct a 2-functor F from (Pre-Orb) to the 2-category (Grp) of proper \'etale effective groupoid objects over the complex manifolds. Both…
This brief note corrects some errors in the paper quoted in the title, highlights a combinatorial result which may have been overlooked, and points to further improvements in recent literature.
We introduce new Elmendorf constructions for equivariant categories and posets, and we prove that they are compatible with the classical topological one. Our constructions are more concrete than their model-categorical counterparts, and…