Spahn combinatorial shape (Rev #4)

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

References

• This Week’s Finds in Mathematical Physics (Week 242), web (Discussion at the n-Cafe)

• Tom Leinster, higher operads, higher categories, arXiv:math/0305049

• higher topos theory

• André Joyal, The theory of quasicategories and its applications lectures at Simplicial Methods in Higher Categories, (pdf)

• André Joyal, Notes on quasi-categories (pdf).

• Eugenia Cheng, Aaron Lauda, higher-dimensional categories: an illustrated guide book, pdf

• Ieke Moerdijk, Bertrand Toen, simplicial methods for operads and algebraic geometry