A presentable six-functor formalism satisfying cohomological purity extends to Ind- and Pro-categories, defining motivic stable homotopy theory for ind-pro algebraic stacks such as the Hecke stack.
Six-Functor Formalisms II : The $\infty$-categorical compactification
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abstract
This paper is part of a series of articles in which we reproduce the statements regarding the abstract six-functor formalism developed by Liu-Zheng. In this paper, we prove a theorem, which is an $\infty$-categorical version for defining the exceptional pushforward functor in an abstract-six functor formalism. The article describes specific combinatorial simplicial sets related to compactifications and pullback squares. This theorem plays a key role in constructing the abstract six-functor formalism, which will be discussed in the forthcoming article.
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Abstract Six-Functor Formalisms: Extension to Ind- and Pro- Categories and Functorial Cohomological Purity
A presentable six-functor formalism satisfying cohomological purity extends to Ind- and Pro-categories, defining motivic stable homotopy theory for ind-pro algebraic stacks such as the Hecke stack.