1. Isomorphism between objects 2. Goupoïdes Post Views: 224 Post navigation Category defintions & Examples Functor
![In mathematics, especially in category theory and homotopy theory, a groupoid (less often Brandt groupoid or virtual group) generalises the notion of group in several equivalent ways. A groupoid can be seen as a: Group with a partial function replacing the binary operation; Category in which every morphism is invertible. A category of this sort can be viewed as augmented with a unary operation, called inverse by analogy with group theory.[1] Notice that a groupoid where there is only one object is a usual group. Special cases include: Setoids, that is: sets that come with an equivalence relation; G-sets, sets equipped with an action of a group G. Groupoids are often used to reason about geometrical objects such as manifolds. Heinrich Brandt (1927) introduced groupoids implicitly via Brandt](http://3.bp.blogspot.com/-d3nuDNweUgE/VnCEGN__-7I/AAAAAAAAAQY/hXHsbDbcaRA/s1600/8.png "Groupoid category")
