Nuprl Lemma : full-faithful-functor_wf
∀[C,D:SmallCategory]. ∀[F:Functor(C;D)]. (ff-functor(C;D;F) ∈ ℙ)
Proof
Definitions occuring in Statement :
full-faithful-functor: ff-functor(C;D;F),
cat-functor: Functor(C1;C2),
small-category: SmallCategory,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
full-faithful-functor: ff-functor(C;D;F),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
small-category_wf,
cat-functor_wf,
functor-arrow_wf,
functor-ob_wf,
cat-arrow_wf,
biject_wf,
cat-ob_wf,
all_wf
Rules used in proof :
because_Cache,
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
applyEquality,
lambdaEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
lemma_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[C,D:SmallCategory]. \mforall{}[F:Functor(C;D)]. (ff-functor(C;D;F) \mmember{} \mBbbP{})
Date html generated:
2016_05_18-AM-11_52_27
Last ObjectModification:
2015_12_28-PM-02_23_53
Theory : small!categories
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