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A note on model structures on arbitrary Frobenius categories [PDF]
Advances in Mathematics, 2016 We show that there is a model structure in the sense of Quillen on an arbitrary Frobenius category $\F$ such that the homotopy category of this model structure is equivalent to the stable category $\underline{\F}$ as triangulated categories.Comment ...
Li, Zhi-Wei
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Six model categories for directed homotopy [PDF]
Categories and General Algebraic Structures with Applications, 2021 We construct a q-model structure, an h-model structure and an m-model structure on multipointed $d$-spaces and on flows. The two q-model structures are combinatorial and left determined and they coincide with the combinatorial model structures already ...
Philippe Gaucher
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Arrow categories of monoidal model categories [PDF]
MATHEMATICA SCANDINAVICA, 2019 We prove that the arrow category of a monoidal model category, equipped with the pushout product monoidal structure and the projective model structure, is a monoidal model category. This answers a question posed by Mark Hovey, in the course of his work on Smith ideals.
White, David, Yau, Donald
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Enriched Reedy categories [PDF]
, 2015 We define the notion of an enriched Reedy category, and show that if A is a C-Reedy category for some symmetric monoidal model category C and M is a C-model category, the category of C-functors and C-natural transformations from A to M is again a model ...
Angeltveit, Vigleik
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Comparison theorems for Kan, faintly universal and strongly universal derived functors [PDF]
Surveys in Mathematics and its Applications, 2022 We distinguish between faint, weak, strong and strict localizations of categories at morphism families and show that this framework captures the different types of derived functors that are considered in the literature.
Alisa Govzmann +2 more
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A unified representation and transformation of multi-model data using category theory
Journal of Big Data, 2022 The support for multi-model data has become a standard for most of the existing DBMSs. However, the step from a conceptual (e.g., ER or UML) schema to a logical multi-model schema of a particular DBMS is not straightforward.
Pavel Koupil, Irena Holubová
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, 2022 AbstractIn [123] Quillen proposed an axiomatic framework for homotopy theory through the notion of a model structure on a category. Such a structure consists of three distinguished classes of morphisms, calledweak equivalences, fibrations, and cofibrations, required to satisfy several axioms reminiscent of the properties of the corresponding notions in
Gijs Heuts, Ieke Moerdijk
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A neural network model of hippocampal contributions to category learning
eLife, 2023 In addition to its critical role in encoding individual episodes, the hippocampus is capable of extracting regularities across experiences. This ability is central to category learning, and a growing literature indicates that the hippocampus indeed makes
Jelena Sučević, Anna C Schapiro
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The Lifting-Extension Problem for Duchain Complexes of Dwyer and Kan
Demonstratio Mathematica, 2015 A duchain complex of W. Dwyer and D. Kan is a common extension of the notions of a chain complex and a cochain complex.
Spaliński Jan
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Semi-Supervised Instance-Segmentation Model for Feature Transfer Based on Category Attention
Sensors, 2022 In the task of image instance segmentation, semi-supervised instance segmentation algorithms have received constant research attention over recent years.
Hao Wang +7 more
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