5
votes
0answers
224 views

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 ...
4
votes
1answer
230 views

Definition of enriched caterories or internal homs without using monoidal categories.

I know this question may seem nonsensical at first but let me exlain what i have in mind: In enriched category theory we define categories enriched over a monoidal category $(\mathcal{V},\otimes, ...
25
votes
0answers
582 views

Enriched Categories: Ideals/Submodules and algebraic geometry

While working through Atiyah/MacDonald for my final exams I realized the following: The category(poset) of ideals $I(A)$ of a commutative ring A is a closed symmetric monoidal category if endowed ...