  The study of homotopy theoretic phenomena in the language of type theory is
sometimes loosely called `synthetic homotopy theory'. Homotopy theory in type
theory is only one of the many aspects of homotopy type theory, which also
includes the study of the set theoretic semantics (models of homotopy type
theory and univalence in a meta-theory of sets or categories), type theoretic
semantics (internal models of homotopy type theory), and computational
semantics, as well as the study of various questions in the internal language
of homotopy type theory which are not necessarily motivated by homotopy theory,
or questions related to the development of formalized libraries of mathematics
based on homotopy type theory. This thesis concerns the development of
synthetic homotopy theory.
