Results 11 to 20 of about 5,909 (88)
Homotopy monomorphisms and H-splitting in loop space fibrations
Topology and its Applications, 2008 Let \(X,\) \(Y\) and \(Z\) be \(H\)-spaces and \(f:Y\to X\) and \(g:Z\to X\) be \(H\)-maps. The composite \(Y\times Z\to X\times X\to X\) is called an \(H\)-splitting if it is a homotopy equivalence and an \(H\)-map. The author considers here the special case of \(\Omega B\times\Omega F\to\Omega E,\) where \(p:E\to B\) is a fibration with fibre \(i:F ...
Luofei Liu
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Epimorphism plus monomorphism implies equivalence in the homotopy category
Journal of Pure and Applied Algebra, 1975 David Handel
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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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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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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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On the Algebraic Classification of Module Spectra [PDF]
, 2011 Using methods developed by Franke, we obtain algebraic classification results for modules over certain symmetric ring spectra ($S$-algebras). In particular, for any symmetric ring spectrum $R$ whose graded homotopy ring $\pi_*R$ has graded global ...
Patchkoria, Irakli
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Modeling (∞,1)$(\infty,1)$‐categories with Segal spaces
Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.Abstract In this paper, we construct a model structure for (∞,1)$(\infty,1)$‐categories on the category of simplicial spaces, whose fibrant objects are the Segal spaces. In particular, we show that it is Quillen equivalent to the models of (∞,1)$(\infty,1)$‐categories given by complete Segal spaces and Segal categories.
Lyne Moser, Joost Nuiten
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The shift‐homological spectrum and parametrising kernels of rank functions
Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.Abstract For any compactly generated triangulated category, we introduce two topological spaces, the shift spectrum and the shift‐homological spectrum. We use them to parametrise a family of thick subcategories of the compact objects, which we call radical.
Isaac Bird +2 more
wiley +1 more source
$C^*$-algebraic drawings of dendroidal sets
, 2019 In recent years the theory of dendroidal sets has emerged as an important framework for higher algebra. In this article we introduce the concept of a $C^*$-algebraic drawing of a dendroidal set. It depicts a dendroidal set as an object in the category of
Mahanta, Snigdhayan
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