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- W4387431472 abstract "We define and study homotopy groups of cubical sets. To this end, we give four definitions of homotopy groups of a cubical set, prove that they are equivalent, and further that they agree with their topological analogues via the geometric realization functor. We also provide purely combinatorial proofs of several classical theorems, including: product preservation, commutativity of higher homotopy groups, the long exact sequence of a fibration, and Whitehead’s theorem. This is a companion paper to our “Cubical setting for discrete homotopy theory, revisited” in which we apply these results to study the homotopy theory of simple graphs." @default.
- W4387431472 created "2023-10-08" @default.
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- W4387431472 date "2023-10-01" @default.
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- W4387431472 title "Homotopy groups of cubical sets" @default.
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- W4387431472 doi "https://doi.org/10.1016/j.exmath.2023.125518" @default.
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