# Tagged Questions

For questions about simplicial sets (functors from simplex category to sets), simplicial (co)algebras and simplicial objects in other categories; geometric realization, model structures, Dold-Kahn correspondence etc. Please do not use for questions about geometry of simplices nor about ...

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### How to define a transported version of the simplex $X = \{x \in \mathbb{R}^n_{+}| \sum\limits_{i = 1}^n x_i = 1\}$?

Let the simplex in $\mathbb{R}^n$ be denoted as $$X = \{x \in \mathbb{R}^n_{+}| \sum\limits_{i = 1}^n x_i = 1\}$$ So it looks like: I want to take a point $\bar x \in X$ (red dot) And drag it to ...
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### singular homology of a simplicial complex [duplicate]

On Page 108 of the book Algebraic Topology, Allen Hatcher, the singular homology of a topological space $X$ is defined to be the homology of the chain complex by setting the $n$-chains $C_n(X)$ as the ...
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### Sheaves of Simplicial Rings?

Could someone provide me a reference for a treatment of sheaves of simplicial commutative rings? As in simplicial sheaves with a ring structure.
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### Simplicial homotopy's exponential law

The following was cited from Simplicial Homotopy Theory by John F. Jardine and Paul Gregory Goerss. We have an adjunction $$\hom_{\mathbf{S}}(X\times Y,Z)\simeq \hom_{\mathbf{S}}(Y,\mathbf{Hom}(X,Z))$$...
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### Enriching categories of simplicial objects

Let $C$ be a cocomplete category and $Simp(C)=C^{\triangle^{op}}$ the category of simplicial objects in $C$. I want to show that $Simp(C)$ is simplicially enriched but I don't understand how the ...
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### Question about limit of cosimplicial diagram associated with a sheaf

Let $F$ be a presheaf of sets on the usual topological site. Let $\left\{U_i\rightarrow U\right\}$ be covering of $U$. On the second page of Hypercovers and Simplicial Presheaves the authors write the ...
### Ratio of dimension sizes in a pure $2$-dimensional simplicial complex
I'm listening to Alex Lubotzky's YouTube lecture on Cohomology and Computer Science, and during a proof he makes the claim: $\displaystyle\frac{|X(2)|}{|X(1)|} \sim \frac{n}{3}$, where $n$ is the ...