# Retract of a loop

From Groupprops

This article defines a property that can be evaluated for a subloop of a loop| View other such properties

ANALOGY: This is an analogue in algebra loop of a property encountered in group. Specifically, it is a [[{{{new specific context}}} property]] analogous to the subloop property: retract

View other analogues of retract | View other analogues in algebra loops of subloop properties (OR, View as a tabulated list)

## Definition

A subloop of an algebra loop is termed a **retract** of if there is a homomorphism of loops such that for all .

## Relation with other properties

### Stronger properties

Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
---|---|---|---|---|

Direct factor of a loop | |FULL LIST, MORE INFO |