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.) Masbaum-Vaintrob trees (m.v.t.) Of course, while the latter three … Continue reading

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Vignettes. Part 1. Complete Graphs via right-adjoints to forgetting.

The following is widely-, though not widely-enough-known. 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

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Shaping by pruning: one shape-changing leaf implies infinitely-many shapes obtainable by finitely-often 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

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