## 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 tree category ### $\square$ the cube category ### $\Theta$ 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