DGA algebras as a Quillen model category relations to shm maps

DOI10.1016/0022-4049(78)90009-9zbMath0409.55018OpenAlexW2025220897MaRDI QIDQ1259052

Hans Jørgen Munkholm

Publication date: 1978

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-4049(78)90009-9

zbMATH Keywords

Closed Model CategoryDifferential Graded Augmented AlgebrasHomotopy CategoryStrongly Homotopy Multiplicative Maps

Mathematics Subject Classification ID

Rational homotopy theory (55P62) Localization and completion in homotopy theory (55P60) Abstract and axiomatic homotopy theory in algebraic topology (55U35) Eilenberg-Moore spectral sequences (55T20)

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Hopf Algebras up to Homotopy ⋮ Homotopy theory of homotopy algebras ⋮ Decompositions of certain loop spaces. ⋮ Derived representation schemes and cyclic homology ⋮ The Adams-Hilton model for a fibration over a sphere ⋮ Daniel Quillen, the father of abstract homotopy theory ⋮ Cubical homotopical algebra and cochain algebras ⋮ Hochschild cohomology of a strongly homotopy commutative algebra ⋮ Cyclicity in homotopy algebras and rational homotopy theory ⋮ L.S.-category in a model category ⋮ On the algebraic approximation of Lusternik--Schnirelmann category. ⋮ Derived representation schemes and Nakajima quiver varieties ⋮ Comparison of MacLane, Shukla and Hochschild cohomologies ⋮ Injective resolutions of \(BG\) and derived moduli spaces of local systems ⋮ On the homotopy structure of strongly homotopy associative algebras

Cites Work

• The Eilenberg-Moore spectral sequence and strongly homotopy multiplicative maps
• shm maps of differential algebras. I: A characterization up to homotopy
• On the extended functoriality of Tor and Cotor
• Homotopical algebra
• The rational homotopy of a wedge
• Rational homotopy theory
• On 𝑃𝐿 de Rham theory and rational homotopy type
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