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What to call the natural transformation in the Yoneda lemma

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#category-theory #terminology #functors #yoneda-lemma #representable-functor
112
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How can we quickly verify naturality?

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#category-theory #yoneda-lemma
95
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How to go about proving theorems about category theory?

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#proof-writing #category-theory #natural-transformations #yoneda-lemma
82
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If $f:Y \to X$ is a mono in $\textsf{Set}^{\mathbb{C}^{op}}$, then $f$ factors uniquely through $Y \xrightarrow{g} A \stackrel{i}{\hookrightarrow} X$.

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#category-theory #yoneda-lemma #monomorphisms
104
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How does the 2-yoneda lemma exactly work

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#category-theory #adjoint-functors #yoneda-lemma #2-categories
150
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Dualising the Yoneda lemma.

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#category-theory #functors #natural-transformations #yoneda-lemma
83
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Presheaf is terminal iff it maps every object to a singleton

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#category-theory #sheaf-theory #natural-transformations #yoneda-lemma #terminal-objects
115
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A particular presheaf on a small category. What if it's representable?

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#category-theory #functors #yoneda-lemma #presheaves
71
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If the presheaf Hom$_\mathcal{C}(- \times A, B) : \mathcal{C}^\text{op} \to \textbf{Set}$ is representable, then $\mathcal{C}$ is ccc

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#category-theory #functors #yoneda-lemma #presheaves
78
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Usage of Yoneda lemma to show ${\rm Lan}_K \dashv \mathcal{E}^K$

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#category-theory #adjoint-functors #yoneda-lemma #kan-extensions
122
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Contravariant Yoneda lemma

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#category-theory #yoneda-lemma
88
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Two definitions of categorical limits

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#abstract-algebra #category-theory #definition #limits-colimits #yoneda-lemma
268
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Left-adjoint to Yoneda embedding

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#abstract-algebra #category-theory #examples-counterexamples #adjoint-functors #yoneda-lemma
155
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Stacky Yoneda lemma

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#differential-geometry #category-theory #yoneda-lemma
127
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Automorphism group of the functor $P:G\text{-FinSet} \to \text{Set}$

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#category-theory #limits-colimits #profinite-groups #yoneda-lemma

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