  The bicategory of Landau-Ginzburg models denoted by LGK possesses adjoints
and this helps in explaining a certain duality that exists in the setting of
Landau-Ginzburg models in terms of some specified relations. The construction
of LGK is reminiscent of, but more complex than, the construction of the
bicategory of associative algebras and bimodules. In this paper, we review this
complex but very inspiring construction in order to expose it more to pure
mathematicians. In particular, we spend some time explaining the intricate
construction of unit morphisms in this bicategory from a new vantage point.
Besides, we briefly discuss how this bicategory could be constructed in more
than one way using the variants of the Yoshino tensor product. Furthermore,
without resorting to Atiyah classes, we prove that the left and right unitors
in this bicategory have direct right inverses but do not have direct left
inverses.

Category Theory