Steenrod homology
Yu. T. Lisitsa, S. Mardešić (1986)
Banach Center Publications
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Yu. T. Lisitsa, S. Mardešić (1986)
Banach Center Publications
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Daryl George (1984)
Fundamenta Mathematicae
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Philippe Gaucher (2002)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Barr, Michael (2006)
Theory and Applications of Categories [electronic only]
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Krzysztof K. Putyra (2014)
Banach Center Publications
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We create a framework for odd Khovanov homology in the spirit of Bar-Natan's construction for the ordinary Khovanov homology. Namely, we express the cube of resolutions of a link diagram as a diagram in a certain 2-category of chronological cobordisms and show that it is 2-commutative: the composition of 2-morphisms along any 3-dimensional subcube is trivial. This allows us to create a chain complex whose homotopy type modulo certain relations is a link invariant. Both the original and...
Alan Robinson (1987)
Mathematische Zeitschrift
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Stanislaw Betley (1992)
Commentarii mathematici Helvetici
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Barr, Michael (2005)
Theory and Applications of Categories [electronic only]
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Bauer, Friedrich W. (2001)
Homology, Homotopy and Applications
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M. V. Mielke (1993)
Commentationes Mathematicae Universitatis Carolinae
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In this paper we extend the Eilenberg-Steenrod axiomatic description of a homology theory from the category of topological spaces to an arbitrary category and, in particular, to a topos. Implicit in this extension is an extension of the notions of homotopy and excision. A general discussion of such homotopy and excision structures on a category is given along with several examples including the interval based homotopies and, for toposes, the excisions represented by “cutting out” subobjects....
Dung Yung Yan (1995)
Mathematische Zeitschrift
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Fred Richman (1976)
Fundamenta Mathematicae
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