ScalingStacks

Lemma 3.8. The Reidemeister I chain maps $R1_{\pm}\colon\left\llbracket L\right\rrbracket\to\left\llbracket L^{0}_{\pm}\right\rrbracket$ and $R1^{-1}_{\pm}\colon\left\llbracket L^{x}_{\pm}\right\rrbracket\to\left\llbracket L^{\prime}\right\rrbracket$ preserve the internal and external homological degrees individually. Moreover, their only non-zero components are in external homological grading zero.