Jensen hierarchy

The Grothendieck construction is an auxiliary construction used in the mathematical field of category theory.

Let

$F:C\to \text{Sets}$

be a functor from any small category to the category of sets. The Grothendieck construction for $F$ is the category $\mathrm{\Gamma }(F)$ whose objects are pairs $(c,x)$, where $c\in C$ is an object and $x\in F(c)$ is an element, and for which the set ${\text{Hom}}_{\mathrm{\Gamma }(F)}((c_1,x_1),(c_2,x_2))$ is the set of morphisms $f:c_1\to c_2$ in $C$ such that $F(f)(x_1)=x_2$.

References

• Mac Lane and Moerdijk, Sheaves in Geometry and Logic, pp. 44.