Theorems · Definition · category theory

CategoryTheory.Limits.SequentialProduct.cone

{C : Type u_1} →
  {M N : ℕ → C} →
    [inst : CategoryTheory.Category.{v_1, u_1} C] →
      (f : (n : ℕ) → M n ⟶ N n) →
        [inst_1 : CategoryTheory.Limits.HasCountableProducts C] →
          CategoryTheory.Limits.Cone
            (CategoryTheory.Functor.ofOpSequence (CategoryTheory.Limits.SequentialProduct.functorMap f))

The cone over the tower `` ⋯ → ∏_{n < m} M n × ∏_{n ≥ m} N n → ⋯ → ∏ N ` with cone point ∏ M. This is a limit cone, see CategoryTheory.Limits.SequentialProduct.isLimit`.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.SequentialProduct

Cited by

5 results in Mathlib

Foundations

Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasCountableProducts