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15
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Show that the bijection $\text{Cat}(A \times B, C) \cong \text{Cat}(A, C^B)$ is natural

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#abstract-algebra #category-theory #adjoint-functors
50
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Is every sub-Hopf algebra a Frobenius extension?

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#adjoint-functors #hopf-algebras
470
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Connection between universal properties and the existence of a left adjoint

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#abstract-algebra #category-theory #adjoint-functors #functors #universal-property
127
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Counit of adjunction between $\mathbf{Vect}_k$ and $\mathbf{Set}$

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#logic #category-theory #proof-explanation #universal-algebra #adjoint-functors
243
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Proving the equivalence of two definitions of adjoint functors without using the triangle identities

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#abstract-algebra #category-theory #solution-verification #adjoint-functors #universal-property
76
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Mnemonics for memorizing $\overline{g:F(A)\to B}=G(g)\circ \eta_A$ and $\overline {f:A\to G(B)}=\epsilon_B\circ F(f)$

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#abstract-algebra #category-theory #adjoint-functors #mnemonic
49
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Characterization of adjunctions via universal elements

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#abstract-algebra #category-theory #solution-verification #adjoint-functors
52
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Simplicial orbit realization functor.

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#homotopy-theory #simplicial-stuff #adjoint-functors
144
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Constructing the left adjoint to the forgetful functor $G:\textbf{Vect}_\mathbb{C}\to\textbf{Vect}_\mathbb{R}$

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#category-theory #adjoint-functors
74
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Well-definedness of left adjoint functors

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#algebraic-geometry #category-theory #foundations #adjoint-functors
253
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What are the categories whose sheaves are representable?

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#reference-request #category-theory #limits-colimits #adjoint-functors #locally-presentable-categories
204
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Left adjoint to inverse image sheaf

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#category-theory #sheaf-theory #adjoint-functors
233
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Relation between representable functors and adjunction

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#category-theory #adjoint-functors #representable-functor
216
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Unit and counit of adjunction yield a canonical map

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#category-theory #adjoint-functors #cartesian-closed-categories
53
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With $F$ adjoint to $G$ show that exists a functorial morphism $FG\rightarrow 1_D$

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#abstract-algebra #adjoint-functors #functors

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