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Connections between graphs and sheaves. (English) Zbl 1443.08005

Summary: In this paper, we discuss a method to construct a global sheaf space using graphs via Maximal compatibility blocks (MCB’s) and we proposed the correspondence between graphs and sheaves. Further we discussed the sheaf constructions for various graphs using MCB’s and vice-versa. We also presented some graph theoretical examples for the construction of sheaves.

MSC:

08A99 Algebraic structures
05C99 Graph theory
18F20 Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects)
03G15 Cylindric and polyadic algebras; relation algebras
Full Text: DOI

References:

[1] A. Wolf,Sheaf representations of arithmetical algebras, Mem. Amer. Math. Soc.148 (1974) 85-97. · Zbl 0274.08009
[2] B. A. Davey,sheaf spaces and sheaves of universal algebras, Math. Z., (4)134 (1973), 275-290. · Zbl 0259.08002
[3] G. Malcolm,Sheaves, Objects and Distributed Systems, Electronic Notes in Theoretical Computer Science, Elsevier,225(2009) 3-19. · Zbl 1336.68184
[4] J.Friedman,Sheavesongraphsandtheirhomologicalinvariants, arXiv:1104.2665v1 [math.Co] 14 April 2011.
[5] J. M. Curry,Sheaves, Cosheaves and Applications, arXiv:1303.3255v2 [math. AT] 17 December 2014.
[6] K. H. Hofmann,Representation of algebras by continuous sections, Bull. Amer.math. Soc. (3)78(1972), 291-373. · Zbl 0237.16018
[7] M.P.K.Kishore,R.V.G.Ravi Kumar,and P.Vamsi Sagar.,Costruction of sheaves by tolerance relations, Asian-European Journal of Mathematics, World Scientific Publishing Company,(2)9(2016), 1650035 (8 pages), DOI: 10.1142/S1793557116500352 · Zbl 1336.14013
[8] M. Robinsoin,Understanding networks and their behaviors using Sheaf theory, arXiv:1308.4621v1 [math AT] 21 August 2013.
[9] M. Robinson,Topological signal processing, Springer, 2016. · Zbl 1294.94001
[10] S. D. Comer,Representation by algebras of sections over Boolean spaces, Pacific J. Math.38(1971),29 -38. · Zbl 0219.08002
[11] U.M.Swamy,RepresentationofUniversalalgebrasbysheaves, Proc.Amer.Math. Soc,45(1974), 55-58. · Zbl 0261.08003
[12] U.
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