combinatorial shape

One way to define higher structures is via functors on categories of combinatorial shapes (also called categories of geometric shapes).

Other approaches to define higher structures are by enrichment? or by internalization?.

General theory

Reedy categories

Interaction with model structures, generalized- and elegant Reedy categories

Characterizations of cells

Functorial characterization

Recursive characterization


Δ\Delta the simplex category

Ω\Omega the globe category

TT the tree category

\square the cube category

Θ n\Theta_n Joyal’s (disc) category

Θ A\Theta_A

where AA is an ω\omega-operad and Θ A\Theta_A is a dense subcategory of the category of A̲\underline A-algebras. This is diecussed in Berger.

Γ\Gamma Segal’s category



Functorial images of combinatorial shape categories

Constraints on the functor

Nerves, Realization and Segal conditions

Model structures and presentation of higher structures


Last revised on November 16, 2012 at 18:08:16. See the history of this page for a list of all contributions to it.