Standard t-structures

2025/04/10 by Haine, Peter J., Porta, Mauro, Teyssier, Jean-Baptiste
#Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.07473

Abstract

We provide a general construction of induced t-structures, that generalizes standard t-structures for ∞-categories of sheaves. More precisely, given a presentable ∞-category X and a presentable stable ∞-category E equipped with an accessible t-structure τ= (E_{≥ 0}, E_{≤ 0}), we show that X ⊗ E is equipped with a canonical t-structure whose coconnective part is given in X ⊗ E_{≤ 0}. When X is an ∞-topos, we give a more explicit description of the connective part as well.

Related

• Constant families of t-structures on derived categories of coherent sheaves
• The t-structures generated by objects
• T-model structures on chain complexes of presheaves
• Self-dual T-structure
• Notions of (∞,1)-sites and related formal structures