Free adjunction of morphisms (bibtex)

by Lutz Schröder and Horst Herrlich

Abstract:

We develop a general setting for the treatment of extensions of categories by means of freely adjoined morphisms. To this end, we study what we call composition graphs, i.e. large graphs with a partial binary operation on which we impose only rudimentary requirements. The quasicategory thus obtained contains the quasicategory of all categories as a full reflective subquasicategory; we characterize composition graphs for which this reflexion is of a particularly simple nature. This leads to the concept of semicategory; we apply semicategories to solve characterization problems concerning absolutely initial sources, absolute monosources and potential sections. For instance, we show that in any category, the absolutely initial sources are precisely the sources that contain a section.

Reference:

Lutz Schröder and Horst Herrlich: Free adjunction of morphisms, In Applied Categorical Structures, 8, pp. 595–606, 2000. [preprint]

Bibtex Entry:

@Article{SchroderHerrlich00c,
  author = {Lutz Schr{\"o}der and Horst Herrlich},
  title = {Free adjunction of morphisms},
  year = {2000},
  journal = {Applied Categorical Structures},
  volume = {8},
  pages = {595--606},
  keywords = {semicategory absolutely initial morphism absolute monomorphism graph category section},
  comment = { <a href = "http://www8.informatik.uni-erlangen.de/~schroeder/papers/freeadj.pdf"> [preprint] </a>},
  abstract = {We develop a general setting for the treatment of extensions of categories by means of freely adjoined morphisms. To this end, we study what we call composition graphs, i.e. large graphs with a partial binary operation on which we impose only rudimentary requirements. The quasicategory thus obtained contains the quasicategory of all categories as a full reflective subquasicategory; we characterize composition graphs for which this reflexion is of a particularly simple nature. 

This leads to the concept of semicategory; we apply semicategories to solve characterization problems concerning absolutely initial sources, absolute monosources and potential sections. For instance, we show that in any category, the absolutely initial sources are precisely the sources that contain a section.
},
}