Nuprl Lemma : presheaf_map_wf
∀[C:SmallCategory]. ∀[A,B:Presheaf(C)]. (A ⟶ B ∈ 𝕌')
Proof
Definitions occuring in Statement :
presheaf_map: A ⟶ B,
presheaf: Presheaf(C),
small-category: SmallCategory,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
presheaf_map: A ⟶ B,
subtype_rel: A ⊆r B,
presheaf: Presheaf(C)
Lemmas referenced :
nat-trans_wf,
op-cat_wf,
small-category-subtype,
type-cat_wf,
presheaf_wf,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[A,B:Presheaf(C)]. (A {}\mrightarrow{} B \mmember{} \mBbbU{}')
Date html generated:
2020_05_20-AM-07_57_44
Last ObjectModification:
2017_10_04-PM-06_00_25
Theory : small!categories
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