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 :
top: Top,
all: ∀x:A. B[x],
uimplies: b supposing a,
so_apply: x[s],
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
cat-monad: Monad(C),
monad-functor: monad-functor(M),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
small-category_wf,
cat-monad_wf,
top_wf,
functor-comp_wf,
id_functor_wf,
nat-trans_wf,
subtype_rel_product,
cat-functor_wf,
pi1_wf_top
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
axiomEquality,
voidEquality,
voidElimination,
isect_memberEquality,
lambdaFormation,
independent_isectElimination,
because_Cache,
productEquality,
lambdaEquality,
applyEquality,
rename,
setElimination,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[M:Monad(C)]. (monad-functor(M) \mmember{} Functor(C;C))
Date html generated:
2017_01_19-PM-02_57_58
Last ObjectModification:
2017_01_17-AM-11_29_21
Theory : small!categories
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