Amalgamations of Categories

Canadian mathematical bulletin

关键词: category;    pushout;    amalgamation;   

DOI  :  10.4153/CMB-2009-030-5

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We consider the pushout of embedding functors in $Cat$, thecategory of small categories.We show that if the embedding functors satisfy a 3-for-2property, then the induced functors to the pushout category arealso embeddings. The result follows from the connectedness ofcertain associated slice categories. The condition is motivatedby a similar result for maps of semigroups. We show that ourtheorem can be applied to groupoids and to inclusions of fullsubcategories. We also give an example to show that the theoremdoes not hold when theproperty only holds for one of the inclusion functors, or when itis weakened to a one-sided condition.

【 授权许可】

Unknown