Results 41 to 50 of about 9,368,793 (360)
Transactions of the American Mathematical Society, 1981 Quillen has constructed a K K -theory K ∗ C {K_{\ast }}C for nice categories, one of which is the category of projective R R -modules. We construct a theory K V
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On the (co)homology theory of index category
Journal of the Egyptian Mathematical Society, 2011 In the present work the different types of regular index categories are given. The related cohomology groups of some of these categories are studied. We give some properties of index category related with monoid and algebra over it.
Yasien Ghallab Gouda
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The 2-category theory of quasi-categories
Advances in Mathematics, 2015 84 pages; v4, final journal version, expository improvements suggested by referee and a handful of new lemmas streamlining the presentation in sections 4-6; an appendix, establishing the equivalence between the join and fat join construction, has been cut from v4 but can be found in v3.
Emily Riehl, Dominic Verity
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THE MAGNITUDE OF A METRIC SPACE: FROM CATEGORY THEORY TO GEOMETRIC MEASURE THEORY [PDF]
, 2016 Magnitude is a numerical isometric invariant of metric spaces, whose definition arises from a precise analogy between categories and metric spaces. Despite this exotic provenance, magnitude turns out to encode many invariants from integral geometry and ...
T. Leinster, M. Meckes
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The Brauer category and invariant theory [PDF]
Journal of the European Mathematical Society, 2015 A category of Brauer diagrams, analogous to Turaev's tangle category, is introduced, a presentation of the category is given, and full tensor functors are constructed from this category to the category of tensor representations of the orthogonal group O (V) or the symplectic group Sp
Gustav I. Lehrer, Ruibin Zhang
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Self-move and Other-move: Quantum Categorical Foundations of Japanese [PDF]
Journal of Interdisciplinary Sciences, 2023 This work contributes toward the larger goal of creating a Quantum Natural Language Processing (QNLP) translation program. It contributes original diagrammatic representations of the Japanese language based on previous work on the English language ...
Ryder Dale Walton
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Dendroidal sets as models for homotopy operads [PDF]
, 2011 The homotopy theory of infinity-operads is defined by extending Joyal's homotopy theory of infinity-categories to the category of dendroidal sets. We prove that the category of dendroidal sets is endowed with a model category structure whose fibrant ...
Cisinski, Denis-Charles, Moerdijk, Ieke
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Category Free Category Theory and Its Philosophical Implications [PDF]
, 2016 There exists a dispute in philosophy, going back at least to Leibniz, whether is it possible to view the world as a network of relations and relations between relations with the role of objects, between which these relations hold, entirely eliminated ...
M. Heller
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An Invitation to Applied Category Theory
, 2019 Category theory is unmatched in its ability to organize and layer abstractions and to find commonalities between structures of all sorts. No longer the exclusive preserve of pure mathematicians, it is now proving itself to be a powerful tool in science ...
Brendan Fong, David I. Spivak
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Topological Superconductors and Category Theory [PDF]
, 2015 We give a pedagogical introduction to topologically ordered states of matter, with the aim of familiarizing the reader with their axiomatic topological quantum field theory description.
A. Bernevig, T. Neupert
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