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Displaying similar documents to “Reflexive and dihedral (co)homology of a pre-additive category.”

Preserving homology.

Barr, Michael (2006)

Theory and Applications of Categories [electronic only]

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A 2-category of chronological cobordisms and odd Khovanov homology

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...

Steenrod homology

Yu. T. Lisitsa, S. Mardešić (1986)

Banach Center Publications

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Topos based homology theory

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....