Related papers: Grothendieck's Equality vs Voevodsky's Equality

Consider a complex affine variety $\tilde V$ and a real analytic Zariski-dense submanifold V of $\tilde V$. We compare modules over the ring $O (\tilde V)$ of regular functions on $\tilde V$ with modules over the ring $C^\infty (V)$ of…

Fix a noetherian scheme S. For any flat map f: X->Y of separated essentially-finite-type perfect S-schemes we define a canonical derived-category map c(f):\H(X)->f^!\H(Y), the fundamental class of f, where \H(Z) is the (pre-)Hochschild…

Using the idea of the degree of a smooth mapping between two manifolds of the same dimension we present here the topological (homotopical) classification of the mappings between spheres of the same dimension, vector fields, monopole and…

We study the relation of two frameworks for multiplicative homotopy theories: Presentably symmetric monoidal $\infty$-categories and combinatorial symmetric monoidal model categories. Our main theorem establishes an equivalence of their…

We study cohomology theories of strongly homotopy algebras, namely $A_\infty, C_\infty$ and $L_\infty$-algebras and establish the Hodge decomposition of Hochschild and cyclic cohomology of $C_\infty$-algebras thus generalising previous work…

We propose a new framework for the study of homological properties for (compactly generated) triangulated categories such as regularity, finiteness of global or finitistic dimension, gorensteinness or injective generation and the relation…

We introduce global model categories as a general framework to capture several phenomena in global equivariant homotopy theory. We then construct genuine stabilizations of these, generalizing the usual passage from unstable to stable global…

We consider the interplay of point counts, singular cohomology, \'etale cohomology, eigenvalues of the Frobenius and the Grothendieck ring of varieties for two families of varieties: spaces of rational maps and moduli spaces of marked,…

Polynomials in a category have been studied as a generalization of the traditional notion in mathematics. Their construction has recently been extended to higher groupoids, as formalized in homotopy type theory, by Finster, Mimram, Lucas…

We study homotopy theory of the wheeled prop controlling Poisson structures on arbitrary formal graded finite-dimensional manifolds and prove, in particular, that Grothendieck-Teichmueller group acts on that wheeled prop faithfully and…

The moduli space of isometry classes of Riemannian structures on a smooth manifold was emphasized by J.A.Wheeler in his superspace formalism of quantum gravity. A natural question concerning it is: What is a natural topology on such moduli…

We discuss some finite homogeneous structures, addressing the question of universality of their automorphism groups. We also study the existence of so-called Kat\v{e}tov functors in finite categories of embeddings or homomorphisms.

This paper discusses the development of synthetic cohomology in Homotopy Type Theory (HoTT), as well as its computer formalisation. The objectives of this paper are (1) to generalise previous work on integral cohomology in HoTT by the…

Multi-sorted algebraic theories provide a formalism for describing various structures on spaces that are of interest in homotopy theory. The results of Badzioch and Bergner showed that an interesting feature of this formalism is the…

The objective of this work is to reconsider the schematization problem of [6], with a particular focus on the global case over Z. For this, we prove the conjecture [Conj. 2.3.6][15] which gives a formula for the homotopy groups of the…

It is now very known how the subprojectivity of modules provides a fruitful new unified framework of the classical projectivity and flatness. In this paper, we extend this fact to the category of complexes by generalizing and unifying…

We introduce the notion of balanced pair of additive subcategories in an abelian category. We give sufficient conditions under which the balanced pair of subcategories gives rise to equivalent homotopy categories of complexes. As an…

We show that if the canonical left semi-model structure on the category of Grothendieck $n$-groupoids exists, then it satisfies the homotopy hypothesis, i.e. the associated $(\infty,1)$-category is equivalent to that of homotopy $n$-types,…

We examine the quantum symmetric and exterior algebras of finite-dimensional \uqg-modules first systematically studied by Berenstein and Zwicknagl, and resolve some questions that they raised. We show that the difference (in the…

In this paper, we have obtained a generalization of the Grothendieck's theorem for the space of continuous mappings $C_{\lambda,\mu}(X,Y)$ where $Y$ is a complete uniform space with the uniformity $\mu$ endowed with the topology of uniform…