krati -ka'i- gismu

x1 represents/is an agent/proxy/stands-in for [absent] x2 in matter(s)/function(s) x3.

Also: on behalf of. See also cmavo list ka'i, jansu, catni, vipsi, pulji.

In definition:

ka'i
krati modal, 1st place represented by ...
seka'i (comp!)
krati modal, 2nd place representingly; on behalf of ...
teka'i (comp!)
krati modal, 2nd place representingly; representing in matter...

In notes:

catni
x1 has authority/is an official in/on/over matter/sphere/persons x2 derived on basis x3.
jansu
x1 is a diplomat/consul representing polity x2 in/at negotiation x3 for function/purpose x4.
pulji
x1 is a police officer/[enforcer/vigilante] enforcing law(s)/rule(s)/order x2.
vipsi
x1 is a deputy/vice/subordinate in aspect [or organization principle] x2 (ka) to principal x3.
brika'i
x1 is a pro-bridi representing predicate relationship x2 with relation x3 among arguments x4.
brodyiolpe
x1 is a mass-individual (myopic singular, Mr Broda); x1, or rather every individual among x1, is logically an individual but represents a plurality and has the properties of what it represents
ceirka'i
x1 is the incarnation/avatar of god x2 of religion x3
cuska'i
x1=k1 is a spokesperson of/speaks on behalf of x2=k2=c1, saying x3=c2 to x4=c3 via expressive medium x5=c4.
ka'irtrusi'o
s1 is the concept of representative democracy (default: political representative democracy) as it applies to the governance of t2 based on the works of thinker(s) s3
kibyka'i
x1 is an Internet avatar/representation of user x2 on website/function x3
sumka'i
x1 is a pro-sumti/pronoun representing x2 as argument of predicate/function x3 filling place x4.
ku'ai'i (exp!)
empty/vacuous selbri
goilka'i
x1 (text / virtual-text-object) is a variable representing x2