Questions tagged [yoneda-lemma]
The yoneda-lemma tag has no usage guidance.
13 questions with no upvoted or accepted answers
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In what context can enriched category theory be done?
There are many possible situations one can do enriched category theory. See https://ncatlab.org/nlab/show/category+of+V-enriched+categories#possible_contexts for a list.
My question is what ...
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Yoneda embedding and Horn sentences
The following is taken from Borceux and Bourn's Mal'cev, Protomodular, Homological, and Semi-Abelian Categories.
Metatheorem 0.1.3. Let $\mathcal P$ be a statement of the form $\varphi\implies \psi$, ...
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When do Kan extensions preserve colimits?
Assume that we have a pair of functors $Y:A \to B$ and $F:A \to C$ where $A$ is an essentially small category, $B,C$ are cocomplete categories and $Y,F$ preserve colimits. Assume also that for some ...
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Regarding a coend calculation in "Pullback preserving functors"
In Rosebrugh and Wood's paper Pullback preserving functors, there is a coend calculation that is mostly straightforward, but contains one step I do not follow. I suspect the context is not important ...
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How to learn about Higher Topoi
I have been learning quasicategory theory in an attempt to understand higher topoi, and I have been trying to look at as many different sources as possible. Higher Topos Theory provides a higher ...
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Does Cantor Bernstein hold in a Closed Symmetric Monoidal Category?
In a closed symmetric monoidal category with $[I,X] \cong X$ for all $X$ is it true that having monomorphisms $m :A \rightarrow B$ and $m: B \rightarrow A$ is enough to imply $A \cong B$ ?
I tried to ...
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Yoneda Lemma from the perspective of "Categories = Partial Semigroups"
Categories can equivalently be defined as a special kind of partial semigroup: We impose some axioms on a partial semigroup that ensure the existence of well behaved "(partial) identity elements&...
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All functors "are" left adjoints, and applications?
Throughout this thread, let us assume smallness.
All functors "are" left adjoints
Let $D \xrightarrow{F} C$ be any functor, which induces
$$ D \xrightarrow{F} \hat{C}$$
by compositing the ...
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Is the Kolmogorov-Arnold representation theorem an example of the Yoneda lemma?
From Wikipedia:
https://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Arnold_representation_theorem
In real analysis and approximation theory, the Kolmogorov–Arnold representation theorem (or ...
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Are there any detailed references for the enriched yoneda lemma?
I am just starting out learning enriched category theory, and I am looking for a reference proof of the Yoneda lemma for categories enriched in a monoidal category.
Thank you for your help.
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Is there a bicategorical Yoneda lemma for marked lax transformations?
The bicategorical Yoneda lemma (see [Johnson–Yau, Chapter 8]) states that, given a bicategory $\mathcal{C}$ and a pseudopresheaf $\mathcal{F}\colon\mathcal{C}^{\mathsf{op}}\to\mathsf{Cats}_{\mathsf{2}}...
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Continuity of Kan extension along the Yoneda embedding
Let $\mathcal{C}$ be a category and $h_-: \mathcal{C} \to \mathrm{Set}^{\mathcal{C}^{op}}$ be the Yoneda embedding. Let $\mathcal{A}$ be a cocomplete category and $F: \mathcal{C} \to \mathcal{A}$ a ...
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Question on definition of closed embedding of affine group schemes
$\DeclareMathOperator\Hom{Hom}$I am reading Introduction to affine group schemes by Waterhouse. In the second chapter he defines a closed embedding in the following way. Let $G = \Hom_k(A,-)$ and $H'= ...
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