All Questions
Tagged with enriched-category-theory mg.metric-geometry
4
questions
1
vote
0
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151
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Reference request: a class of matrices leading to interesting metric geometry
For $0 \le A \in GL(n,\mathbb{R})$, let $Aw = \Delta(A)$, where $\Delta$ denotes the map taking a matrix to a vector of its diagonal entries and/or forming a diagonal matrix from a vector, according ...
1
vote
0
answers
98
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Pointwise convergence in Lawvere metric spaces
In the formalism of Lawvere metric spaces, we have that the distance in the hom-space $[X,Y]$ is given by:
$$
d(f,g) = \sup_{x\in X} d(f(x),g(x)) .
$$
Therefore, a sequence of functions $f_n:X\to Y$ ...
6
votes
0
answers
345
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Enriched Categories: Metric Spaces, Monoidal Endofunctors and Lipschitz-Continuous Maps.
In the introduction to the reprint of "Metric spaces, generalized logic and closed categories" Lawvere talks about the following situation:
Let $\mathbb R_+$ denote $\mathbb R_{\geq 0}^\infty$. Every ...
2
votes
1
answer
178
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Reference Request(Enriched Categories): Metric on Lipschitz Continuous Functions
If we consider metric spaces to be categories enriched over $\mathbb R_{\geq 0}$, the object corresponding to presheaves should be lipschitz-continuous functions $\operatorname{Lip^ 1}(M, \mathbb R_{\...