Results 51 to 60 of about 1,060 (227)
Detecting model categories among Quillen categories using homotopies
Theory and Applications of Categories, 2022 A Quillen category is a category equipped with two weak factorization systems \((\mathcal{C},\mathcal{F}_t)\) and \((\mathcal{C}_t,\mathcal{F})\) such that \(\mathcal{C}_t\subset \mathcal{C}\) and \(\mathcal{F}_t\subset \mathcal{F}\). Every model category gives rise to a Quillen category. The paper gives conditions so that a Quillen category gives rise
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Homotopy coherent category theory [PDF]
Transactions of the American Mathematical Society, 1997 This article is an introduction to the categorical theory of homotopy coherence. It is based on the construction of the homotopy coherent analogues of end and coend, extending ideas of Meyer and others. The paper aims to develop homotopy coherent analogues of many of the results of elementary category theory, in particular it handles a homotopy ...
Cordier, Jean-Marc, Porter, Timothy
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On computing local monodromy and the numerical local irreducible decomposition
Transactions of the London Mathematical Society, Volume 13, Issue 1, December 2026.Abstract Similarly to the global case, the local structure of a holomorphic subvariety at a given point is described by its local irreducible decomposition. Geometrically, the key requirement for obtaining a local irreducible decomposition is to compute the local monodromy action of a generic linear projection at the given point, which is always well ...
Parker B. Edwards +1 more
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$A_{\infty}$-structures in monoidal DG categories and strong homotopy unitality [PDF]
, 2023 Rina Anno +2 more
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Sheafifiable homotopy model categories, II
Journal of Pure and Applied Algebra, 2001 [For part I, cf. \textit{T. Beke}, Math. Proc. Camb. Philos. Soc. 129, No. 3, 447-475 (2000; Zbl 0964.55018)]. Suppose one has a category \({\mathcal C}\) and a functor \(F\) from \({\mathcal C}\) to \({\mathcal S}\)\textit{ets}. Then there is an induced functor from the category \(s{\mathcal C}\) of simplicial objects in \({\mathcal C}\) to simplicial
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Model categories with simple homotopy categories
Theory and Applications of Categories, 2015 In the present article, we describe constructions of model structures on general bicomplete categories. We are motivated by the following question: given a category $\mathcal{C}$ with a subcategory $w\mathcal{C}$ closed under retracts, when is there a model structure on $\mathcal{C}$ with $w\mathcal{C}$ as the subcategory of weak equivalences? We begin
Droz, Jean-Marie, Zakharevich, Inna
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Local equivalence and refinements of Rasmussen's s‐invariant
Journal of Topology, Volume 19, Issue 1, March 2026.Abstract Inspired by the notions of local equivalence in monopole and Heegaard Floer homology, we introduce a version of local equivalence that combines odd Khovanov homology with equivariant even Khovanov homology into an algebraic package called a local even–odd (LEO) triple.
Nathan M. Dunfield +2 more
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Periodic self maps and thick ideals in the stable motivic homotopy category over $\mathbb{C}$ at odd primes [PDF]
, 2021 Sven-Torben Stahn
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The ∞$\infty$‐categorical reflection theorem and applications
Journal of Topology, Volume 19, Issue 1, March 2026.Abstract We prove an ∞$\infty$‐categorical version of the reflection theorem of AdÁmek and Rosický [Arch. Math. 25 (1989), no. 1, 89–94]. Namely, that a full subcategory of a presentable ∞$\infty$‐category that is closed under limits and κ$\kappa$‐filtered colimits is a presentable ∞$\infty$‐category.
Shaul Ragimov, Tomer M. Schlank
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The DNA of Calabi–Yau Hypersurfaces
Fortschritte der Physik, Volume 74, Issue 2, February 2026.Abstract Genetic Algorithms are implemented for triangulations of four‐dimensional reflexive polytopes, which induce Calabi–Yau threefold hypersurfaces via Batyrev's construction. These algorithms are shown to efficiently optimize physical observables such as axion decay constants or axion–photon couplings in string theory compactifications.
Nate MacFadden +2 more
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