  Lenses encode protocols for synchronising systems. We continue the work begun
by Chollet et al. at the Applied Category Theory Adjoint School in 2020 to
study the properties of the category of small categories and asymmetric delta
lenses. The forgetful functor from the category of lenses to the category of
functors is already known to reflect monos and epis and preserve epis; we show
that it preserves monos, and give a simpler proof that it preserves epis.
Together this gives a complete characterisation of the monic and epic lenses in
terms of elementary properties of their get functors.
  Next, we initiate the study of coequalisers of lenses. We observe that not
all parallel pairs of lenses have coequalisers, and that the forgetful functor
from the category of lenses to the category of functors neither preserves nor
reflects all coequalisers. However, some coequalisers are reflected; we study
when this occurs, and then use what we learned to show that every epic lens is
regular, and that discrete opfibrations have pushouts along monic lenses.
Corollaries include that every monic lens is effective, every monic epic lens
is an isomorphism, and the class of all epic lenses and the class of all monic
lenses form an orthogonal factorisation system.
