University of Tehran
Journal of Sciences, Islamic Republic of Iran
10161104
5
2
1994
09
01
THE INTERNAL IDEAL LATTICE IN THE
TOPOS OF MSETS

31184
EN
Journal Article
1970
01
01
We believe that the study of the notions of universal algebra modelled in an
arbitarry topos rather than in the category of sets provides a deeper
understanding of the real features of the algebraic notions. [2], [3], [4], [S], [6],
[7], [13], [14] are some examples of this approach. The lattice Id(L) of ideals of
a lattice L (in the category of sets) is an important ingredient of the category of
lattices. In this paper, we construct the (internal) ideal lattice T(A) of a lattice
A in the topos of Msets for a monoid M. The process of the construction of
Y(A) is so that it can also be done in any arbitrary topos whose ingredients are
known. Finally, we consider the lattice structure of T(A) for some special kind
of lattices A in the topos of Msets and show, among other things, that if A is
an internally complete MBoolean algebra then Y(A) is an MStone lattice
https://jsciences.ut.ac.ir/article_31184_677e95291946119127dfdad1089697ad.pdf