simplicial resolution

- homotopy hypothesis-theorem
- delooping hypothesis-theorem
- periodic table
- stabilization hypothesis-theorem
- exactness hypothesis
- holographic principle

- (n,r)-category
- Theta-space
- ∞-category/∞-category
- (∞,n)-category
- (∞,2)-category
- (∞,1)-category
- (∞,0)-category/∞-groupoid
- n-category = (n,n)-category
- 2-category, (2,1)-category
- 1-category
- 0-category
- (?1)-category?
- (?2)-category?

- n-poset = (n-1,n)-category
- n-groupoid = (n,0)-category

- categorification/decategorification
- geometric definition of higher category
- Kan complex
- quasi-category
- simplicial model for weak ∞-categories?

- algebraic definition of higher category
- stable homotopy theory

The concept of *resolution* in homotopy theory specialized to simplicial homotopy theory is “simplicial resolution”.

the following needs attention

In any ambient category or $\infty$-category $C$ that admits a notion of colimit or weak colimit, a *simplicial resolution* of an object $c \in C$ is a simplicial object $y_\bullet : \Delta^{op} \to C$ such that it realizes $c$ as a colimit

$c \simeq colim_{[k]} y_k
\,.$

The term is also used for a Reedy fibrant replacement of a constant simplicial object in a model category; see also resolution.

- In an (infinity,1)-topos ?ech cover? $C(U) \stackrel{\simeq}{\to} X$ induced by a cover $(U = \coprod_i U_i) \to X$ is a simplicial resolution of $X$.

Simplicial resolutions in the context of presentable (infinity,1)-categories are discussed in section 6.1.4 of

(below lemma 6.1.4.3)

Revised on September 27, 2017 01:22:18
by Tim Porter
(2a01:cb08:818d:3e00:3476:67d1:dbb5:ad17)