List questions from simplicial-stuff

Published on 10 May 2026 - 16:33

770

Views

The normalized chain complex of a simplicial set

Published on 13 Apr 2026 - 9:03

84

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If matching maps of a cosimplicial space are fibrations up to degree $n$, does the $n$-th partial totalization have the 'correct' homotopy type?

Published on 15 Apr 2026 - 8:18

79

Views

Classifying Space of a Category Contractible

Published on 26 Apr 2026 - 8:43

683

Views

Let $K$ be a simplicial complex (that need not be finite). Prove $|K|$ is Hausdorff.

Published on 10 May 2026 - 16:34

49

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How to see that $S(\sigma) = \text{Hom}_{\Delta}(\sigma, [0,1])$ maps to the category $\tilde{\Delta}^{\text{op}}$.

Published on 10 May 2026 - 12:34

109

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There's an equivalence of simplicial categories $\Delta \to \tilde{\Delta}^{\text{op}}$.

Published on 14 Apr 2026 - 21:57

194

Views

Pushout-product of anodyne extensions is again anodyne

Published on 12 Apr 2026 - 8:43

73

Views

Simplicial Sets as a Lawvere Theory

Published on 13 Apr 2026 - 1:42

593

Views

Tensor product of exact complexes is exact

Published on 16 Apr 2026 - 0:31

200

Views

Issue with Coequalizer Definition of the Horn of a Simplex

Published on 10 Apr 2026 - 1:30

74

Views

Triangulation of fiber bundles

Published on 10 May 2026 - 16:11

156

Views

Equivalence between the Dwyer-Kan loop groupoid and the fundamental groupoid

Published on 10 May 2026 - 16:05

215

Views

Why does Spivak define the realization functor from fuzzy simplicial sets to extended pseudo metric spaces the way he does?

Published on 05 May 2026 - 6:06

103

Views

Proof all anodyne extensions come from saturating $\Lambda_I^0({}, M)$

Published on 10 May 2026 - 16:55

List Question

Horn of a Simplicial Set

The normalized chain complex of a simplicial set

If matching maps of a cosimplicial space are fibrations up to degree $n$, does the $n$-th partial totalization have the 'correct' homotopy type?

Classifying Space of a Category Contractible

Let $K$ be a simplicial complex (that need not be finite). Prove $|K|$ is Hausdorff.

How to see that $S(\sigma) = \text{Hom}_{\Delta}(\sigma, [0,1])$ maps to the category $\tilde{\Delta}^{\text{op}}$.

There's an equivalence of simplicial categories $\Delta \to \tilde{\Delta}^{\text{op}}$.

Pushout-product of anodyne extensions is again anodyne

Simplicial Sets as a Lawvere Theory

Tensor product of exact complexes is exact

Issue with Coequalizer Definition of the Horn of a Simplex

Triangulation of fiber bundles

Equivalence between the Dwyer-Kan loop groupoid and the fundamental groupoid

Why does Spivak define the realization functor from fuzzy simplicial sets to extended pseudo metric spaces the way he does?

Proof all anodyne extensions come from saturating $\Lambda_I^0({}, M)$

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