## Abstract

Category theory starts with the observation that many properties of mathematical systems can be unified and simplified by a presentation with diagrams of arrows. Each arrow *f* : *X* → *Y* represents a function; that is, a set *X*, a set *Y*, and a rule *x* ↦ *f x* which assigns to each element *x* ∈ *X* an element *f x* ∈ *Y*; whenever possible we write *f x* and not *f*(*x*), omitting unnecessary parentheses.

## Keywords

Abelian Group Topological Space Diagram Commute Category Theory Universal Property
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer Science+Business Media New York 1978