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Flasque model structures for simplicial presheaves. (English) Zbl 1116.18008
Flasque model structures on simplicial sheaves were defined by K. S. Brown and S. M. Gersten [Lect. Notes Math. 341, 266–292 (1973; Zbl 0291.18017)]. The author studies flasque model structures on simplicial presheaves. They form an intermediate structure between projective and injective model structures in the sense of J. F. Jardine [Can. Math. Bull. 49, 407–413 (2006; Zbl 1107.18007)]. As an example of application the author shows that motivic stable homotopy groups commute with filtered colimits [see also Proposition 9.3 in D. Dugger and D. C. Isaksen, Algebr. Geom. Topol. 5, 615–652 (2005; Zbl 1086.55013)].

MSC:
18G55 Nonabelian homotopical algebra (MSC2010)
14F42 Motivic cohomology; motivic homotopy theory
18F20 Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects)
55U35 Abstract and axiomatic homotopy theory in algebraic topology
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References:
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