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Results tagged with enriched-category-theory
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user 24563
2
votes
0
answers
133
views
Tensor product of objectwise weak homotopy equivalences of $\mathcal{M}$-spaces
I consider the enriched category $[\mathcal{M}^{op},\mathrm{Top}]$ of enriched functors (I call them $\mathcal{M}$-spaces) from the enriched small category $\mathcal{M}^{op}$ to the enriched category …
- 3,901
1
vote
0
answers
66
views
Tensored and cotensored simplicial comma category
To transfer a tensored and cotensored simplicially enriched structure from a category $\mathcal{C}$ to $(\mathcal{C}\downarrow Z)$, we define $(X\to Z)\otimes K$ by the composite $(X\otimes K \to X \ …
- 3,901
2
votes
0
answers
142
views
When this coend is invariant up to homotopy?
It is a follow-up of my question Calculation of the homotopy colimit of a diagram of spaces which was badly formulated.
Consider a fixed diagram $D:I^{op}\to {\rm Top}$ where ${\rm Top}$ is
a conveni …
- 3,901