---

Step * 1 2 of Lemma cubical-nerve_wf


1. X : SmallCategory
⊢ λI,J,f,F. functor-comp(poset-functor(I;J;f);F) ∈ I:(Cname List)
  ⟶ J:(Cname List)
  ⟶ name-morph(I;J)
  ⟶ Functor(poset-cat(I);X)
  ⟶ Functor(poset-cat(J);X)
BY
{ (RepeatFor 4 ((FunExt THENW Auto)) THEN Reduce 0) }

1
1. X : SmallCategory
2. I : Cname List
3. J : Cname List
4. x : name-morph(I;J)
5. x1 : Functor(poset-cat(I);X)
⊢ functor-comp(poset-functor(I;J;x);x1) ∈ Functor(poset-cat(J);X)

---

Latex:

---

Latex:

1.  X  :  SmallCategory
\mvdash{}  \mlambda{}I,J,f,F.  functor-comp(poset-functor(I;J;f);F)  \mmember{}  I:(Cname  List)
    {}\mrightarrow{}  J:(Cname  List)
    {}\mrightarrow{}  name-morph(I;J)
    {}\mrightarrow{}  Functor(poset-cat(I);X)
    {}\mrightarrow{}  Functor(poset-cat(J);X)


By

---

Latex:
(RepeatFor  4  ((FunExt  THENW  Auto))  THEN  Reduce  0)

---

Home Index