Some recent advances in topological Hochschild homology

A Mathew - Bulletin of the London Mathematical Society, 2022 - Wiley Online Library
Some recent advances in topological Hochschild homology - Mathew - 2022 - Bulletin of the
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[HTML][HTML] Constructible sheaves on schemes

T Hemo, T Richarz, J Scholbach - Advances in Mathematics, 2023 - Elsevier
We present a uniform theory of constructible sheaves on arbitrary schemes with coefficients
in topological or even condensed rings. This is accomplished by defining lisse sheaves to …

Differential cohomology: categories, characteristic classes, and connections

A Amabel, A Debray, PJ Haine - arxiv preprint arxiv:2109.12250, 2021 - arxiv.org
We give an overview of differential cohomology from a modern, homotopy-theoretic
perspective in terms of sheaves on manifolds. Although modern techniques are used, we …

Yoneda's lemma for internal higher categories

L Martini - arxiv preprint arxiv:2103.17141, 2021 - arxiv.org
Yoneda's lemma for internal higher categories Page 1 YONEDA’S LEMMA FOR INTERNAL
HIGHER CATEGORIES LOUIS MARTINI Abstract. We develop some basic concepts in the theory …

Topological exodromy with coefficients

M Porta, JB Teyssier - arxiv preprint arxiv:2211.05004, 2022 - arxiv.org
We improve the exodromy equivalence of MacPherson, Treumann and Lurie in several
ways: first, we allow stratified spaces that have locally weakly contractible strata, rather than …

Adams spectral sequences and Franke's algebraicity conjecture

I Patchkoria, P Pstrągowski - arxiv preprint arxiv:2110.03669, 2021 - arxiv.org
To any well-behaved homology theory we associate a derived $\infty $-category which
encodes its Adams spectral sequence. As applications, we prove a conjecture of Franke on …

From nonabelian basechange to basechange with coefficients

PJ Haine - arxiv preprint arxiv:2108.03545, 2021 - arxiv.org
The goal of this paper is to explain when basechange theorems for sheaves of spaces imply
basechange for sheaves with coefficients in other presentable $\infty $-categories. We …

Presenting the topological stratified homotopy hypothesis

L Waas - arxiv preprint arxiv:2403.07686, 2024 - arxiv.org
This article is concerned with three different homotopy theories of stratified spaces: The one
defined by Douteau and Henriques, the one defined by Haine, and the one defined by Nand …

Pyknotic objects, I. Basic notions

C Barwick, P Haine - arxiv preprint arxiv:1904.09966, 2019 - arxiv.org
Pyknotic objects are (hyper) sheaves on the site of compacta. These provide a convenient
way to do algebra and homotopy theory with additional topological information present. This …

Combinatorial models for stratified homotopy theory

L Waas - arxiv preprint arxiv:2403.06280, 2024 - arxiv.org
This paper is part of a series of three articles with the objective of investigating a stratified
version of the homotopy hypothesis in terms of semi-model structures that interact well with …