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Category Archives: Structure theory
Higher Trees Today. Part 0.
For the time being, the installments of the serial ‘Higher Trees Today’ will focus on three kinds of higher trees: Contractible Spaces of Choices (c.s.c.) Diestel–Oum decompositions (d.o.d.) Kalai trees (k.t.) MasbaumVaintrob trees (m.v.t.) Of course, while the latter three … Continue reading
Posted in expository, Higher trees, Mathematics, News, Olds, Research, Simplicial complexes, Structure theory
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Vignettes. Part 1. Complete Graphs via rightadjoints to forgetting.
The following is widely, though not widelyenoughknown. Let a category of graphs of your choice. Probably any reasonable category of graphs will work for you, mutatis mutandis, as they say, provided that the morphisms of are (at least easily interpretable … Continue reading
Posted in Category Theory, Mathematics, Olds, Structure theory, Vignettes.
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Shaping by pruning: one shapechanging leaf implies infinitelymany shapes obtainable by finitelyoften chopping off leaves.
We start with the shape of rayless trees. Our first goal is to prove the following statement. Proposition 1.2 (known since the 1980s). Suppose is an infinite rayless tree with one distinguished vertex, called its root. If there exists at … Continue reading
Posted in Structure theory
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