The shift on the category of triangles #

In this file, it is shown that if C is a preadditive category with a shift by , then the category of triangles Triangle C is also endowed with a shift. We also show that rotating triangles three times identifies with the shift by 1.

The shift on the category of triangles was also obtained by Adam Topaz, Johan Commelin and Andrew Yang during the Liquid Tensor Experiment.

The shift functor Triangle C ⥤ Triangle C by n : ℤ sends a triangle to the triangle obtained by shifting the objects by n in C and by multiplying the three morphisms by (-1)^n.

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