Nuprl Lemma : counit-unit-adjunction_wf
∀[A,B:SmallCategory]. ∀F:Functor(A;B). ∀G:Functor(B;A). (F -| G ∈ Type)
Proof
Definitions occuring in Statement :
counit-unit-adjunction: F -| G,
cat-functor: Functor(C1;C2),
small-category: SmallCategory,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
counit-unit-adjunction: F -| G,
member: t ∈ T,
nat-trans: nat-trans(C;D;F;G),
id_functor: 1,
functor-comp: functor-comp(F;G),
top: Top,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
prop: ℙ,
pi2: snd(t)
Lemmas referenced :
cat-functor_wf,
small-category_wf,
nat-trans_wf,
functor-comp_wf,
id_functor_wf,
ob_mk_functor_lemma,
arrow_mk_functor_lemma,
counit-unit-equations_wf,
cat-ob_wf,
cat-arrow_wf,
functor-ob_wf,
pi1_wf_top,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
setEquality,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesis,
hypothesisEquality,
productEquality,
productElimination,
setElimination,
rename,
sqequalRule,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairEquality,
functionExtensionality,
applyEquality,
functionEquality,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination
Latex:
\mforall{}[A,B:SmallCategory]. \mforall{}F:Functor(A;B). \mforall{}G:Functor(B;A). (F -| G \mmember{} Type)
Date html generated:
2017_10_05-AM-00_51_47
Last ObjectModification:
2017_07_28-AM-09_20_38
Theory : small!categories
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