Questions tagged [simplicial-stuff]

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-Kan correspondence etc. Please do not use for questions about geometry of simplices nor about triangulations.

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On proving that the geometric realization of a simplicial set is a CW complex

As the title states, I am trying to prove that the geometric realization of a simplicial set $X : \Delta^{op} \to \mathsf{Set}$ is always a CW complex. I apologize in advance for asking more than one ...
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What's the difference between an anodyne map and a trivial monomorphism?

This sounds silly but they seem the same to me and I can't find any reference confirming or denying this. The argument in my head goes like this: In the standard model structure on simplicial sets, ...
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Does categorical equivalence commute with colimit?

Lurie defines $\mathfrak{C}:Set_\Delta \rightarrow Cat_\Delta$ the functor from simplicial sets to simplicially enriched categories. And defines: Simplicial sets $X$ are considered to be ...
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Characterization of maps into joins of simplices

This is on page 67, Lem 23.14 of Rezk's notes. I can intuitively see why this is true but cannot write this out neatly. By computing component wise we may attempt to construct $f$ given a set of ...
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I cant simplify this A’B’C + A’BC + A’BC’ + AB’C + ABC boolean expression to A'B+C

I have to get this expression A’B’C + A’BC + A’BC’ + AB’C + ABC to A'B+C. I did this but i cant finish itm i dont know how to. A’B’C + A’BC + A’BC’ + AB’C + ABC A'B(C+C')+C(A'B'+AB'+AB) A'B+C(A'B'+...
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Weak $n$-Category

I'm trying to obtain an intuition for weak n-categories based on explanations from: https://en.wikipedia.org/wiki/Higher_category_theory#Weak_higher_categories https://ncatlab.org/nlab/show/n-...
In Prop 3.1.2 in Cisinski's Higher Categories and Homotopical Algebra, he claims $l(r(\Lambda_I(\{\}, M)) = l(r(\Lambda_I^0(\{\}, M))$, where $M$ is the cellular model and (defined in 2.4.14), $\... 0answers 45 views Why does Spivak define the realization functor from fuzzy simplicial sets to extended pseudo metric spaces the way he does? In Spivak's paper on metric realization of fuzzy simplicial sets, he sends a fuzzy$n$-simplex of strength$a$to the set$$\{(x_0,x_1,\dots,x_n) \in \mathbb{R^{n+1}} |x_0+x_1+\dots+x_n = -\lg(a) \}$...
Let $X$ be a homotopy 1-type (a space with vanishing homotopy groups above degree one). It is a classical fact that $X$ can be recovered completely from its fundamental groupoid. On the the other ...