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ASSet

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Category theory

Homotopy theory

homotopy theory, (∞,1)-category theory, homotopy type theory

flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed

models: topological, simplicial, localic, …

see also algebraic topology

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Definition

The category sSet +sSet_+ of augmented simplicial sets is the category of presheaves on the augmented version of the simplex category Δ a\Delta_a:

sSet +:=Set Δ a op. sSet_+ := Set^{\Delta^{op}_a} \,.

This is the category whose objects are augmented simplicial sets and whose morphisms are the evident morphisms between these.

Applications

The join of simplicial sets is most naturally defined via a construction on augmented simplicial sets.

category: category

Revised on November 4, 2010 08:48:44 by Urs Schreiber (87.212.203.135)