Results 1 to 10 of about 72 (72)
Homological epimorphisms, homotopy epimorphisms and acyclic maps [PDF]
Forum Mathematicum, 2020 Abstract We show that the notions of homotopy epimorphism and homological epimorphism in the category of differential graded algebras are equivalent. As an application we obtain a characterization of acyclic maps of topological spaces in terms of induced maps of their chain algebras of based loop spaces.
Joseph Chuang, Andrey Lazarev
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Analytification, localization and homotopy epimorphisms
Bulletin des Sciences Mathématiques, 2022 We study the interaction between various analytification functors, and a class of morphisms of rings, called homotopy epimorphisms. An analytification functor assigns to a simplicial commutative algebra over a ring $R$, along with a choice of Banach structure on $R$, a commutative monoid in the monoidal model category of simplicial ind-Banach $R ...
Oren Ben-Bassat, Devarshi Mukherjee
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Homotopy epimorphisms and derived tate’s acyclicity for commutative C*-algebras
The Quarterly Journal of Mathematics, 2022 Abstract We study homotopy epimorphisms and covers formulated in terms of derived Tate’s acyclicity for commutative $C^*$-algebras and algebras of continuous functions valued in non-Archimedean valued fields. We prove that a homotopy epimorphism between commutative $C^*$-algebras precisely corresponds to a closed immersion between the ...
Federico Bambozzi, Tomoki Mihara
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Note on Epimorphisms and Monomorphisms in Homotopy Theory [PDF]
Proceedings of the American Mathematical Society, 1984 We study epimorphisms e : X → X e:X \to X and monomorphisms m : X → X m:X \to X in the pointed homotopy category of path-connected CW-spaces.
Hilton, Peter, Roitberg, Joseph
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Homotopy epimorphisms in homotopy pullbacks
Topology and its Applications, 1994 The authors prove that homotopy epimorphisms are preserved under homotopy pullback. (A map \(f: X\to Y\) of pointed path-connected CW-spaces is a homotopy epimorphism, if given \(u,v: Y\to Z\), \(u\circ f\simeq v\circ f\) implies \(u\simeq v\).) The proof makes use of \textit{M. Mather}'s first cube theorem [Can. J. Math.
Hong, Lin, Wenhuai, Shen
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Epimorphisms and monomorphisms in homotopy [PDF]
Proceedings of the American Mathematical Society, 1992 The main result of this note is the following: Theorem A. If f : X → Y f:X \to Y is an epimorphism of H C W ∗ \mathcal {H}\mathcal {C}{\mathcal {W}^*} , the ...
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Homotopy-epimorphisms, homotopy-monomorphisms and homotopy-equivalences
Topology and its Applications, 1992 In a general category, a morphism which is both an epimorphism and a monomorphism need not be an equivalence. However, the authors prove that it is in the case of the homotopy category of pointed path-connected CW- spaces. In fact, they obtain this result as a corollary of a variant of a classical theorem of J. H. C. Whitehead that they prove.
Dyer, Eldon, Roitberg, Joseph
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Homotopy epimorphisms and Lusternik-Schnirelmann category [PDF]
Proceedings of the American Mathematical Society, 1975 This paper examines the relationship of the LusternikSchnirelmann category and related numerical homotopy invariants to the epimorphisms in the homotopy category. The results are of the form: if N is a numerical homotopy invariant and f: X -f Y is an epimorphism, then under certain hypotheses N(X) > N(Y).
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On weak epimorphisms in homotopy theory [PDF]
Pacific Journal of Mathematics, 1986 A weak epimorphism e is a morphism such that if \(g\circ e=0\) then \(g=0\). This notion is the Eckmann-Hilton dual to weak monomorphism. Ganea exhibited examples, in the pointed homotopy category (PHC), of weak monomorphisms that are not monomorphisms.
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Homological epimorphisms and homotopy epimorphisms
, 2019 We show that the notions of homotopy epimorphism and homological epimorphism in the category of differential graded algebras are equivalent. As an application we obtain a characterization of acyclic maps of topological spaces in terms of induced maps of their chain algebras of based loop spaces.
Chuang, Joe, Lazarev, Andrey
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