Abstract
Informally, a higher category consists of
-
(0)
a collection of objects,
-
(1)
for objects x, y a collection of 1-morphisms between x and y,
-
(2)
for objects x, y and 1-morphisms f, g between x and y a collection of 2-morphisms between f and g,
-
(n)
for every n ≥ 0, a collection of n-morphisms involving analogous data,
together with composition laws that are associative up to coherent homotopy.
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Dyckerhoff, T., Kapranov, M. (2019). Topological 1-Segal and 2-Segal Spaces. In: Higher Segal Spaces. Lecture Notes in Mathematics, vol 2244. Springer, Cham. https://doi.org/10.1007/978-3-030-27124-4_2
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