All Questions
Tagged with enriched-category-theory at.algebraic-topology
7
questions
2
votes
0
answers
129
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 $...
- 3,831
12
votes
1
answer
371
views
What is the right notion of a functor from an internal topological category to a topologically enriched category?
Let $\mathcal{C}$ be a category internal to (some convenient model for) topological spaces (which I will denote by $\mathsf{Top}$). In the question Greg Arone asks:
What is the correct notion of a ...
- 781
8
votes
1
answer
585
views
What is the right notion of a functor from an internal topological category to topological spaces?
Let $\mathcal C=(\mathcal O, \mathcal M)$ be a category internal to topological spaces. Thus $\mathcal O$ and $\mathcal M$ are topological spaces: the space of objects and the space of morphisms ...
- 10.8k
5
votes
1
answer
519
views
Simplicial mapping spaces, stable $\infty$-categories, and triangles
Let $C$ be a stable $\infty$-category (presentable, if you like) and let $map(-,-)$ denote the simplicial mapping space. If $X \to Y \to Z$ is a fiber sequence, and $W$ is an object, when is $map(W,X) ...
1
vote
1
answer
171
views
Colocal Objects in Enriched Bousfield Colocalizations
Let $C$ be a $V$-model category, and $\mathcal{K}$ a set of objects of $C$.
Let me denote (derived) simplicial homotopy function complexes by $\text{Dmap}$
and derived $V$-function complexes by $\text{...
6
votes
1
answer
991
views
Properties of loop space functor from homotopy types to group objects in homotopy types
I am trying to understand some properties of categories enriched in homotopy types, and the following question has become important:
When we take the loop-space of a (connected) homotopy type, we get ...
- 728
5
votes
1
answer
385
views
A Reference on Multicategories with "Internal Hom"
The multicategory of Waldhausen categories is "enriched over itself": the Hom-set of $k$-exact functors can be given a Waldhausen category structure by letting the morphisms be natural transformations,...
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