The Grothendieck construction is a construction used in the mathematical field of category theory.
Let be a functor from any small category to the category of small categories. The Grothendieck construction for is the category (also written or ), with
- objects being pairs , where and ; and
- morphisms in being pairs such that in , and in .
Composition of morphisms is defined by .
- Mac Lane and Moerdijk, Sheaves in Geometry and Logic, pp. 44.
- R. W. Thomason (1979). Homotopy colimits in the category of small categories. Mathematical Proceedings of the Cambridge Philosophical Society, 85, pp 91–109. doi:10.1017/S0305004100055535.