Spahn combinatorial shape (Rev #3, changes)

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General theory

Reedy categories

Interaction with model structures, generalized- and elegant Reedy categories

Characterizations of cells

Functorial characterization

Recursive characterization

Examples

$\Delta$ the simplex category

$\Omega$ the globe category

$T$ the disc tree category

Joyal’s category $\square$$\Theta$ the cube category

Segals category $\Theta$$\Gamma$ Joyal’s category

$\Gamma$ Segal’s category

Opetope

Poset

Functorial images of combinatorial shape categories

Constraints on the functor

Nerves, Realization and Segal conditions

Model structures and presentation of higher structures