Nuprl Lemma : functor-arrow-id
∀[C,D:SmallCategory]. ∀[F:Functor(C;D)].
∀x:cat-ob(C). ((F x x (cat-id(C) x)) = (cat-id(D) (F x)) ∈ (cat-arrow(D) (F x) (F x)))
Proof
Definitions occuring in Statement :
functor-arrow: arrow(F),
functor-ob: ob(F),
cat-functor: Functor(C1;C2),
cat-id: cat-id(C),
cat-arrow: cat-arrow(C),
cat-ob: cat-ob(C),
small-category: SmallCategory,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
apply: f a,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
cat-functor: Functor(C1;C2),
and: P ∧ Q,
mk-functor: Error :mk-functor,
top: Top
Lemmas referenced :
cat-ob_wf,
cat-functor_wf,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalHypSubstitution,
setElimination,
thin,
rename,
productElimination,
sqequalRule,
extract_by_obid,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
hypothesisEquality,
isectElimination,
lambdaEquality,
axiomEquality,
because_Cache
Latex:
\mforall{}[C,D:SmallCategory]. \mforall{}[F:Functor(C;D)]. \mforall{}x:cat-ob(C). ((F x x (cat-id(C) x)) = (cat-id(D) (F x)))
Date html generated:
2020_05_20-AM-07_51_04
Last ObjectModification:
2017_01_10-PM-00_32_26
Theory : small!categories
Home
Index