##  [Category](/category) 

  ##  [Category](https://mathlogic.quantumdictionary.io/category-0) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A collection of objects together with, for each ordered pair of objects X,Y, a set Hom(X,Y) of morphisms and an associative composition law ◦ : Hom(Y,Z)×Hom(X,Y) → Hom(X,Z) plus identity morphisms id_X for each object satisfying id_Y ◦ f = f and f ◦ id_X = f.