Nuprl Lemma : functor-presheaf_wf
∀[C,D:SmallCategory]. ∀F:Functor(C;D). ∀P:Presheaf(D). (functor-presheaf(F;P) ∈ Presheaf(C))
Proof
Definitions occuring in Statement :
functor-presheaf: functor-presheaf(F;P),
presheaf: Presheaf(C),
cat-functor: Functor(C1;C2),
small-category: SmallCategory,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T
Definitions unfolded in proof :
subtype_rel: A ⊆r B,
functor-presheaf: functor-presheaf(F;P),
presheaf: Presheaf(C),
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
small-category_wf,
cat-functor_wf,
presheaf_wf,
op-functor_wf,
type-cat_wf,
small-category-subtype,
op-cat_wf,
functor-comp_wf
Rules used in proof :
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
dependent_functionElimination,
lambdaEquality,
because_Cache,
sqequalRule,
hypothesis,
applyEquality,
hypothesisEquality,
isectElimination,
extract_by_obid,
instantiate,
thin,
sqequalHypSubstitution,
lambdaFormation,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[C,D:SmallCategory]. \mforall{}F:Functor(C;D). \mforall{}P:Presheaf(D). (functor-presheaf(F;P) \mmember{} Presheaf(C))
Date html generated:
2017_10_05-PM-03_34_10
Last ObjectModification:
2017_10_05-AM-11_37_40
Theory : small!categories
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