/usr/share/gap/lib/adjoin.gd is in gap-libs 4r7p5-2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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#W adjoin.gd GAP library Steve Linton
##
##
##
## This file contains the declarations for functions pertaining to
## adjoining an identity element to a semigroup.
##
DeclareCategory("IsMonoidByAdjoiningIdentityElt", IsMultiplicativeElementWithOne and IsAssociativeElement);
DeclareCategory("IsMonoidByAdjoiningIdentity", IsMonoid);
DeclareAttribute("AdjoinedIdentityFamily", IsFamily);
DeclareAttribute("UnderlyingSemigroupFamily", IsFamily);
DeclareAttribute("AdjoinedIdentityDefaultType", IsFamily);
DeclareRepresentation("IsMonoidByAdjoiningIdentityEltRep", IsPositionalObjectRep, 1);
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##
#A MonoidByAdjoiningIdentity( <semigroup> )
##
## this attribute stores the monoid obtained from <semigroup> by adjoining
## an identity. Even if <semigroup> happens to be a monoid, the resultant
## monoid has a new identity adjoined.
##
DeclareAttribute("MonoidByAdjoiningIdentity", IsSemigroup);
###########################################################################
##
#A UnderlyingSemigroupOfMonoidByAdjoiningIdentity( <monoid> )
##
## this attribute stores the original semigroup that <monoid> was made from.
##
DeclareAttribute("UnderlyingSemigroupOfMonoidByAdjoiningIdentity", IsMonoidByAdjoiningIdentity );
###########################################################################
##
#A MonoidByAdjoiningIdentityElt( <elt> )
##
## the result of this function is the corresponding element in the category
## MonoidByAdjoiningIdentityElt with IsOne set to false.
##
DeclareAttribute("MonoidByAdjoiningIdentityElt", IsMultiplicativeElement and IsAssociativeElement);
###########################################################################
##
#A UnderlyingSemigroupOfMonoidByAdjoiningIdentity( <monoidelt> )
##
## this attribute stores the original semigroup element that <monoidelt>
## was made from.
##
DeclareAttribute("UnderlyingSemigroupElementOfMonoidByAdjoiningIdentityElt", IsMonoidByAdjoiningIdentityElt);
#############################################################################
##
#E adjoin.gd . . . . . . . . . . . . . . . . . . . . . . . . . . . ends here
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