sequentialFunctor — Mathlib

English

Definition: the sequentialFunctor J is a functor from Nat^op to J, defined by object and map data coming from sequentialFunctor_obj and sequentialFunctor_map.

Русский

Определение: последовательный функтор J есть функтор Nat^op → J, заданный объектами последовательFunctor_obj и отображениями sequentialFunctor_map.

LaTeX

$$$ \\text{sequentialFunctor } J : \\mathbb{N}^{\\mathrm{op}} \\to J,\\quad \\text{obj}(n) = \\text{sequentialFunctor\\_obj } J n,\\quad \\text{map}(h) = \\text{homOfLE}( \\text{sequentialFunctor\\_map }(J,h)) $$$

Lean4

/-- The initial functor `ℕᵒᵖ ⥤ J`, which allows us to turn cofiltered limits over countable preorders
into sequential limits.
-/
noncomputable def sequentialFunctor : ℕ ⥤ J
    where
  obj n := sequentialFunctor_obj J n
  map h := homOfLE (sequentialFunctor_map J (leOfHom h))

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