Nuprl Lemma : functor-ob_wf
∀[C,D:SmallCategory]. ∀[F:Functor(C;D)]. (ob(F) ∈ cat-ob(C) ⟶ cat-ob(D))
Proof
Definitions occuring in Statement :
functor-ob: ob(F),
cat-functor: Functor(C1;C2),
cat-ob: cat-ob(C),
small-category: SmallCategory,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
pi1: fst(t),
cat-functor: Functor(C1;C2),
functor-ob: ob(F),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
small-category_wf,
cat-functor_wf
Rules used in proof :
because_Cache,
isect_memberEquality,
isectElimination,
lemma_by_obid,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesis,
hypothesisEquality,
productElimination,
rename,
thin,
setElimination,
sqequalHypSubstitution,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[C,D:SmallCategory]. \mforall{}[F:Functor(C;D)]. (ob(F) \mmember{} cat-ob(C) {}\mrightarrow{} cat-ob(D))
Date html generated:
2020_05_20-AM-07_50_50
Last ObjectModification:
2015_12_28-PM-02_23_56
Theory : small!categories
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