mathrm{functor}  F!: quad mathcal{C} to mathcal{D} \ \  begin{matrix}   U  overset{h}{longrightarrow}  &V   overset{g}{longrightarrow}   &W   qquad in textrm{category } mathcal{C}  \  arrowvert   &arrowvert   &arrowvert  \  arrowvert   &arrowvert    &qquad arrowvert : quad F  \    downarrow    &downarrow  &downarrow  \  F( U ) overset{F(h)}{longrightarrow} &F(V)  overset{F(g)}{longrightarrow} &F(W)  quad  in textrm{category } mathcal{D}   end{matrix}

A functor maps dots and arrows (elements and functions), respecting composition.

In category theory, there are no disembodied, “objective” things — every Thing must come with an Interpretation.

About isomorphismes

Argonaut: someone engaged in a dangerous but potentially rewarding adventure.
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