Semantics of lambda calculi by analytic functors and twiners

We overview analytic functors and twiners, and the semantics of lambda
calculi using these concepts.  Historically, analytic functors are
used first by Girard in construction of models of lambda calculi.
Analytic functors are closely related to formal power series, thus
especially to enumerative combinatorics and mathematical analysis.  We
discuss the fixed-point combinator and its analytical interpretation.
Twiners are 2-categorical extension of analytic functors and are
connected to group-theoretical concepts.  We sketch the semantics of
the polymorphic lambda calculus using twiners.