let C be Category; for I being Indexing of C
for T being TargetCat of I
for D, E being Categorial Category
for F being Functor of T,D
for G being Functor of T,E st F = G holds
F * I = G * I
let I be Indexing of C; for T being TargetCat of I
for D, E being Categorial Category
for F being Functor of T,D
for G being Functor of T,E st F = G holds
F * I = G * I
let T be TargetCat of I; for D, E being Categorial Category
for F being Functor of T,D
for G being Functor of T,E st F = G holds
F * I = G * I
let D, E be Categorial Category; for F being Functor of T,D
for G being Functor of T,E st F = G holds
F * I = G * I
let F be Functor of T,D; for G being Functor of T,E st F = G holds
F * I = G * I
let G be Functor of T,E; ( F = G implies F * I = G * I )
assume A1:
F = G
; F * I = G * I
thus F * I =
(F * (I -functor (C,T))) -indexing_of C
by Def17
.=
(G * (I -functor (C,T))) -indexing_of C
by A1, Th2
.=
G * I
by Def17
; verum