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Jozef Przytycki introduced skein modules of 3-manifolds and skein deformation initiating algebraic topology based on knots. We discuss the generalized skein modules of Walker, defined by fields and local relations. Some results by Przytycki are proven in a more general setting of fields defined by decorated cell-complexes in manifolds. A construction of skein theory from embedded TQFT-functors is given, and the corresponding background is developed. The possible coloring of fields by elements of TQFT-modules is discussed for those generalized skein modules. Also an approach of defining skein modules from studying compressions of fields is described.

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This is an author-produced, peer-reviewed version of this article. The final, definitive version of this document can be found online at Banach Center Publications, published by Institute of Mathematics: Polish Academy of Sciences. Copyright restrictions may apply. doi: 10.4064/bc100-0-8

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