Results 1 to 10 of about 5,878 (86)
The Homotopy Category of Monomorphisms Between Projective Modules
Bulletin of the Malaysian Mathematical Sciences Society, 2023 Let $(S, \n)$ be a commutative noetherian local ring and $ω\in\n$ be non-zerodivisor. This paper deals with the behavior of the category $\mon(ω, \cp)$ consisting of all monomorphisms between finitely generated projective $S$-modules with cokernels annihilated by $ω$. We introduce a homotopy category $\HT\mon(ω, \cp)$, which is shown to be triangulated.
Bahlekeh, Abdolnaser +3 more
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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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The homotopy theory of coalgebras over a comonad [PDF]
, 2012 Let K be a comonad on a model category M. We provide conditions under which the associated category of K-coalgebras admits a model category structure such that the forgetful functor to M creates both cofibrations and weak equivalences.
Hess, Kathryn, Shipley, Brooke
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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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Simplicial presheaves of coalgebras [PDF]
, 2011 The category of simplicial R-coalgebras over a presheaf of commutative unital rings on a small Grothendieck site is endowed with a left proper, simplicial, cofibrantly generated model category structure where the weak equivalences are the local weak ...
Brown +11 more
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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 monomorphisms and homotopy pushouts
Topology and its Applications, 1997 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The univalence axiom for elegant Reedy presheaves [PDF]
, 2015 We show that Voevodsky's univalence axiom for intensional type theory is valid in categories of simplicial presheaves on elegant Reedy categories. In addition to diagrams on inverse categories, as considered in previous work of the author, this includes ...
Shulman, Michael
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Waldhausen K-theory of spaces via comodules [PDF]
, 2016 Let $X$ be a simplicial set. We construct a novel adjunction between the categories of retractive spaces over $X$ and of $X_{+}$-comodules, then apply recent work on left-induced model category structures (arXiv:1401.3651v2 [math.AT],arXiv:1509.08154 ...
Hess, Kathryn, Shipley, Brooke
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Semilocalization of epimorphisms and monomorphisms in homotopy theory
Topology and its Applications, 1998 AbstractIn this note, we prove that semilocalization of spaces preserves homotopy monomorphisms and homotopy epimorphisms which induce an isomorphism in fundamental groups, and also prove that homotopy epimorphisms preserve p-nilpotency for every prime or zero p.
Shen, Wenhuai, Zuo, Zaisi
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