高阶同调代数中的结构转移

非点态语境中的同调引理

Homological Lemmas in a Non-pointed Context

本文证明经典同调引理的非点态版本在配备适当偏序单余反射子范畴的正则原模范畴中成立，并给出酉环、布尔代数、海廷代数、MV-代数及其拓扑模型和基本拓扑斯对偶范畴等实例。

Non-abelian and $\varepsilon$-curved homological algebra with arrow categories

Grandis's non-abelian homological algebra generalizes standard homological algebra in abelian categories to \textit{homological categories}, which are a broader class of categories including for example the category of lattices and Galois connections. Here, we prove that if $\mathsf{C}$ is any category with an ideal of null morphisms with respect to which (co)kernels exist, then the arrow category of $\mathsf{C}$ is a homological category. This broadens the applicability of Grandis's framework substantially. In particular, one can form the homology of chain complexes in $\mathsf{C}$ by taking …

Fundamental group functors in descent-exact homological categories

We study the notion of fundamental group in the framework of descent-exact homological categories. This setting is sufficiently wide to include several categories of "algebraic" nature such as the almost abelian categories, the semi-abelian categories, and the categories of topological semi-abelian algebras. For many adjunctions in this context, the fundamental groups are described by generalised Brown-Ellis-Hopf formulae for the integral homology of groups.

同调范畴中的相对理想，及其在 MV-代数中的应用

Relative ideals in homological categories, with an application to MV-algebras

在同调范畴中引入关于忠实保守右伴随的相对理想概念，证明对象可表示为相对理想，并应用于证明 hoops 范畴半阿贝尔性及 MV-代数范畴原模性。

Local and stable homological algebra in Grothendieck abelian categories

We define model category structures on the category of chain complexes over a Grothendieck abelian category depending on the choice of a generating family, and we study their behaviour with respect to tensor products and stabilization. This gives convenient tools to construct and understand triangulated categories of motives and we consider here the case of mixed motives over a regular base scheme.

鞅上同调、holonomy与同调套利

Martingale Cohomology, Holonomy, and Homological Arbitrage

本文引入一个用于范畴滤波的运输上同调框架，通过研究参数化简单形的上同调复形，揭示了循环历史引起的概率扭曲及holonomy结构，提出同调套利作为概率扭曲沿循环产生的全局运输现象。

pro-Lie 波兰阿贝尔群的同调代数

Homological algebra of pro-Lie Polish abelian groups

该研究从同调代数角度研究pro-Lie波兰阿贝尔群，推广型分解并刻画多类波兰阿贝尔群范畴的内射、投射对象及同调维数，推进拓扑群同调代数研究。

同调范畴上一个根的分解系统

The factorization system of a radical on a homological category

研究同调范畴上根的分解系统，借助早期论文中通过伴随转移分解系统的技术，建立了二者的关联。

Homological algebra with locally compact abelian groups

In this article we study locally compact abelian (LCA) groups from the viewpoint of derived categories, using that their category is quasi-abelian in the sense of J.-P. Schneiders. We define a well-behaved derived Hom-complex with values in the derived category of Hausdorff topological abelian groups. Furthermore we introduce a smallness condition for LCA groups and show that such groups have a natural tensor product and internal Hom which both admit derived versions.

Homological algebra in characteristic one

This article develops several main results for a general theory of homological algebra in categories such as the category of sheaves of idempotent modules over a topos. In the analogy with the development of homological algebra for abelian categories the present paper should be viewed as the analogue of the development of homological algebra for abelian groups. Our selected prototype, the category Bmod of modules over the Boolean semifield B is the replacement for the category of abelian groups. We show that the semi-additive category Bmod fulfills analogues of the axioms AB1 and AB2 for abeli…