geometric realization in nLab
In the context of geometric realization of loop stacks and inertia stacks: Ernesto Lupercio, Bernardo Uribe, Section 7.2 of: Inertia ...
geometry of physics -- categories and toposes in nLab
... Geometric realization; The classical model structure on simplicial sets. 9. Basic notions of higher topos theory. Locally presentable ∞ \infty -Categories ...
Grothendieck construction in nLab
be its postcomposition with geometric realization of categories. Then we have a weak homotopy equivalence. | N ( ∫ F ) | ≃ hocolim | N ( F ...
1. Selected writings ... On semi-simplicial sets and their geometric realization: ... Discussion of equivariant configuration spaces of points in ...
Example 4.1. Any undirected graph (loops and/or multiple edges allowed) has a geometric realization as a 1-dimensional CW complex.
A Kan fibration is a morphism of simplicial sets which has the right lifting property with respect to all horn inclusions Λ k [ n ] ↪ Δ n \ ...
Buildings as Metric Spaces ... explains that every building has a geometric realization that admits a CAT(0) metric, which means that it has ...
geometric representation theory in nLab
As an important consequence, the geometric realization of representations often reveals deeper layers of structure in the form of ...
The geometric realization of Q * Q_* is the normalizer of S 1 S^1 in S 3 S^3 (cf. Loday). Just like in the cyclic and dihedral cases, Δ Q \Delta ...
cubical set - exposition in nLab
the geometric realization of cartesian products of cubical sets (see geometric realization below) tends to have the wrong homotopy type: for ...
Eilenberg-Mac Lane space in nLab
Via geometric realization of higher groupoids ... For G G a group, the Eilenberg–Mac Lane space K ( G , 1 ) K(G,1) is the image under the homotopy ...
groupal model for universal principal infinity-bundles in nLab
LieGrpd – the universal G-principal bundle. By applying the geometric realization functor. | − | : ... G -bundle obtained from the realization ...
This, or rather its geometric realization to a rational topological space, is the Sullivan construction. 3. Related concepts. Lie integration ...
It is a model for the path space object of X X , – or rather: the union of all based path space objects for all basepoints x ∈ X 0 x \in X_0 – ...
nLab geometric homotopy groups in an (infinity,1)-topos
Geometric Π ∞ \Pi_\infty of a topological space. Claim. Geometric ... Concrete realizations of this equivalence are discussed in the Examples- ...
Geometric realization is a Reedy cofibrant replacement ... Write ( | − | ⊣ Sing ) : Top → Sing ← | − | ({\vert- \vert} \dashv Sing) : Top\stackrel ...
cohesive (infinity,1)-topos in nLab
the existence of Π \Pi induces a notion of geometric fundamental ∞-groupoid, hence under | − | : ∞ Grpd ≃ |-| : \infty Grpd \simeq Top of ...
... geometric realization adjunction) to the and Quillen model structure on simplicial sets. Parametrized model structures. The parameterized ...
geometry of physics -- groups in nLab
with a discussion of the simplest case of ordinary discrete groups from this natural perspective of regarding them as pointed connected homotopy ...
... geometric realization functor. (Usually, in classical algebraic and geometric topology, the X X here is taken to be a simplicial complex ...