On the Existence of an Orthogonal Factorization System on 1-Cob and 2-Cob

Abstract

We define the category 2-Cob combinatorially and use this definition to prove the existence of an orthogonal factorization system. In the second half of the paper, we define oriented 1-Cob similarly and define a functor from oriented 1-Cob to 2-Cob. After defining this functor, the orthogonal factorization system on 2-Cob is used, in turn, to prove the existence of an orthogonal factorization system on oriented 1-Cob.