English
As above, the monoidal limit compatibility with projections holds for the μ-π relation in the limit of F and G.
Русский
Как и выше, совместимость моноидального предела с проекциями справедлива для отношения μ-π в пределе F и G.
LaTeX
$$$\\mu\\,\\lim F G \\;\\circ\\mathrm{limit}.\\pi_{j} = \\mathrm{limit}.\\pi F j \\otimes_{\\mathrm{mon}} \\mathrm{limit}.\\pi G j$$$
Lean4
/-- When `C` is braided and `tensorLeft c` preserves a limit, then so does `tensorRight k`. -/
instance preservesLimit_of_braided_and_preservesLimit_tensor_left [BraidedCategory C] (c : C)
[PreservesLimit F (tensorLeft c)] : PreservesLimit F (tensorRight c) :=
preservesLimit_of_natIso F (BraidedCategory.tensorLeftIsoTensorRight c)
