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\Hom(A,B) & & \rTo^{\mbox{\scriptsize $\Hom(h,B)$}} & & \Hom(A',B) \\ \dTo<{\mbox{\scriptsize $\Hom(A,f)$}} & & & & \dTo>{\,\mbox{\scriptsize $\Hom(A'...

\mathrm{Hom}(A, B) \ar^{\mathrm{Hom}(h, B)}[r] \ar_{\mathrm{Hom}(A,f)}[d] & \mathrm{Hom}(A', B) \ar^{\mathrm{Hom}(A', f)}[d] \\ \mathrm{Hom}(A, B') \ar_{\mathrm{Hom}(h...

diagram defining adjoint functors. \begin{diagram}[pilespacing=5pt] \Hom_{\scC}(X,GY) & & \rTo^{\mbox{\scriptsize $\Hom(f,Gg)$}} & & \Hom_{\scC}(X',GY') \\ \dEqual<{\Phi_{X...

SVG version of File:AdjointFunctors-01.png  The SVG code is valid.  This vector image was created with MetaPost. Source code InfoField verbatimtex %&latex...

DescriptionGraphical illustration of Hom functor (covariant).svg English: Illustration of H o m ( A , − ) {\displaystyle Hom(A,-)} functor: Fix A ∈ C {\displaystyle...

category A[F −1 ] together with a functor F : A → A[F −1 ] such that F(f ) is an isomorphism for all f in F and any functor G : A → B such that G(f ) is an...

\mathrm{Hom}_{\mathcal{C}}(FY,X) \ar@{=}^{\Phi_{Y,X}}[r] \ar_{\mathrm{Hom}(Fg,f)}[d] & \mathrm{Hom}_{\mathcal{D}}(Y,GX) \ar^{\mathrm{Hom}(g,Gf)}[d]...

should be used in place of this PNG file when not inferior. File:AdjointFunctorsHomSets.png → File:natural phi.svg For more information, see Help:SVG. In...