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Natural isomorphism between the complexification of $V$ and $V^2$, when $V$ is already a complex vector space?

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#linear-algebra #complex-numbers #category-theory #natural-transformations
52
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What are colored morphisms/arrows intended to mean in these diagrams?

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#category-theory #universal-property #morphism #natural-transformations #diagram-chasing
233
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Conjugation Functor from a Groupoid to $\mathbf{Grp}$

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#group-theory #category-theory #higher-category-theory #groupoids #natural-transformations
79
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$\operatorname{Tor}^{\mathbb{Z}}_1(-,-)$ on finite abelian groups is not right exact?

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#abstract-algebra #homological-algebra #exact-sequence #derived-functors #natural-transformations
83
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How many universal cones from $\Delta_{A\times A}$ to D?

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#category-theory #limits-colimits #natural-transformations
32
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Defintion of relative cohomology cross product

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#general-topology #algebraic-topology #homology-cohomology #natural-transformations
77
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Extranatural transformations are a special case of dinatural transformations

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#category-theory #natural-transformations
144
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Natural transformations and canonical maps

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#category-theory #natural-transformations #presheaves
62
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A "natural transformation" in which the "morphisms" are not morphisms

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#category-theory #natural-transformations
80
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'Uniqueness' of adjoint functors

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#category-theory #adjoint-functors #natural-transformations
66
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About the double dual of Lipschitz functions

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#functional-analysis #category-theory #natural-transformations
55
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Proving the existance and uniqueness of the unit of an adjunction

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#abstract-algebra #category-theory #adjoint-functors #functors #natural-transformations
47
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Question on adjoints and natural bijections (Altman & Kleiman Exercise 6.14)

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#category-theory #natural-transformations
114
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Proving naturality in both arguments

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#category-theory #adjoint-functors #natural-transformations
77
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Yoneda lemma for representable profunctors?

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#category-theory #natural-transformations #yoneda-lemma #profunctors

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