Nuprl Lemma : monad-functor_wf
∀[C:SmallCategory]. ∀[M:Monad(C)]. (monad-functor(M) ∈ Functor(C;C))
Proof
Definitions occuring in Statement :
monad-functor: monad-functor(M),
cat-monad: Monad(C),
cat-functor: Functor(C1;C2),
small-category: SmallCategory,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
monad-functor: monad-functor(M),
cat-monad: Monad(C),
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
top: Top
Lemmas referenced :
pi1_wf_top,
cat-functor_wf,
subtype_rel_product,
nat-trans_wf,
id_functor_wf,
functor-comp_wf,
top_wf,
cat-monad_wf,
small-category_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
setElimination,
rename,
applyEquality,
lambdaEquality,
productEquality,
because_Cache,
independent_isectElimination,
lambdaFormation,
isect_memberEquality,
voidElimination,
voidEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[M:Monad(C)]. (monad-functor(M) \mmember{} Functor(C;C))
Date html generated:
2020_05_20-AM-07_58_38
Last ObjectModification:
2017_01_17-AM-11_29_21
Theory : small!categories
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