Cover-preserving order embeddings into Boolean lattices

Wild, Marcel

doi:10.1007/bf00383945

Cited by 11 publications

(2 citation statements)

References 24 publications

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“…Cover preserving order embeddings were considered by Wild in [34] where they give necessary and sufficient conditions guaranteeing cover preserving order embeddings into Boolean lattices. It is an immediate consequence of f : P → Q being an order embedding that f is injective, and thus f is an isomorphism onto f (P ).…”

Section: Functoriality Of Cohomologymentioning

confidence: 99%

Thin Posets, CW Posets, and Categorification

Chandler

2019

Preprint

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Motivated by Khovanov's categorification of the Jones polynomial, we study functors F from thin posets P to abelian categories A. Such functors F produce cohomology theories H * (P, A, F ). We find that CW posets satisfy conditions making them particularly suitable for the construction of such cohomology theories. We consider a category of tuples (P, A, F, c), where c is a certain {1, −1}-coloring of the cover relations in P , and show the cohomology arising from a tuple (P, A, F, c) is functorial, and independent of the coloring c up to natural isomorphism. Such a construction provides a framework for the categorification of a variety of familiar topological/combinatorial invariants: anything expressible as a rank-alternating sum over a thin poset.

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Section: Functoriality Of Cohomologymentioning

confidence: 99%

Thin Posets, CW Posets, and Categorification

Chandler

2019

Preprint

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“…Skorsky also has worked on neighbourhood-preserving embeddings into distributive lattices [156], since this is interesting for the automatic generation of diagrams. Wild [185] had solved the problem for power-set lattices.…”

Section: 3mentioning

confidence: 99%