Nuprl Lemma : monad-unit_wf
∀[C:SmallCategory]. ∀[M:Monad(C)]. ∀[x:cat-ob(C)]. (monad-unit(M;x) ∈ cat-arrow(C) x M(x))
Proof
Definitions occuring in Statement :
monad-unit: monad-unit(M;x),
monad-fun: M(x),
cat-monad: Monad(C),
cat-arrow: cat-arrow(C),
cat-ob: cat-ob(C),
small-category: SmallCategory,
uall: ∀[x:A]. B[x],
member: t ∈ T,
apply: f a
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
so_apply: x[s1;s2;s3],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
all: ∀x:A. B[x],
id_functor: 1,
monad-functor: monad-functor(M),
pi1: fst(t),
pi2: snd(t),
monad-fun: M(x),
nat-trans: nat-trans(C;D;F;G),
cat-monad: Monad(C),
monad-unit: monad-unit(M;x),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
small-category_wf,
cat-monad_wf,
cat-ob_wf,
arrow_mk_functor_lemma,
ob_mk_functor_lemma
Rules used in proof :
because_Cache,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
isectElimination,
hypothesisEquality,
functionExtensionality,
applyEquality,
hypothesis,
voidEquality,
voidElimination,
isect_memberEquality,
dependent_functionElimination,
extract_by_obid,
productElimination,
rename,
thin,
setElimination,
sqequalHypSubstitution,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[C:SmallCategory]. \mforall{}[M:Monad(C)]. \mforall{}[x:cat-ob(C)]. (monad-unit(M;x) \mmember{} cat-arrow(C) x M(x))
Date html generated:
2017_01_19-PM-02_58_14
Last ObjectModification:
2017_01_17-AM-11_46_50
Theory : small!categories
Home
Index