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globularne
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There are 10 letters in GLOBULARNE ( A1B3E1G2L1N1O1R1U1 )
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| Globularne might refer to |
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In category theory, a branch of mathematics, a Globular set is a higher-dimensional generalization of a directed graph. Precisely, it is a sequence of sets * * * * * X * * 0 * * * , * * X * * 1 * * * , * * X * * 2 * * * , * … * * * {\displaystyle X_{0},X_{1},X_{2},\dots } * equipped with pairs of functions * * * * * s * * n * * * , * * t * * n * * * : * * X * * n * * * → * * X * * n * − * 1 * * * * * {\displaystyle s_{n},t_{n}:X_{n}\to X_{n-1}} * such that* * * * * s * * n * * * ∘ * * s * * n * + * 1 * * * = * * s * * n * * * ∘ * * t * * n * + * 1 * * * , * * * {\displaystyle s_{n}\circ s_{n+1}=s_{n}\circ t_{n+1},} * * * * * * * t * * n * * * ∘ * * s * * n * + * 1 * * * = * * t * * n * * * ∘ * * t * * n * + * 1 * * * . * * * {\displaystyle t_{n}\circ s_{n+1}=t_{n}\circ t_{n+1}.} * (Equivalently, it is a presheaf on the category of “globes”.) The letters "s", "t" stand for "source" and "target" and one imagines * * * * * X * * n * * * * * {\displaystyle X_{n}} * consists of directed edges at level n. * A variant of the notion was used by Grothendieck to introduce the notion of an ∞-groupoid. Extending Grothendieck's work, (Maltsiniotis 2010) gave a definition of a weak ∞-category in terms of globular sets. |