Equivalent Definition
The pair of classes of morphisms of C is a factorization system if and only if it satisfies the following conditions:
- Every morphism f of C can be factored as with and
- and
Read more about this topic: Factorization System
Famous quotes containing the words equivalent and/or definition:
“Perhaps basketball and poetry have just a few things in common, but the most important is the possibility of transcendence. The opposite is labor. In writing, every writer knows when he or she is laboring to achieve an effect. You want to get from here to there, but find yourself willing it, forcing it. The equivalent in basketball is aiming your shot, a kind of strained and usually ineffective purposefulness. What you want is to be in some kind of flow, each next moment a discovery.”
—Stephen Dunn (b. 1939)
“Beauty, like all other qualities presented to human experience, is relative; and the definition of it becomes unmeaning and useless in proportion to its abstractness. To define beauty not in the most abstract, but in the most concrete terms possible, not to find a universal formula for it, but the formula which expresses most adequately this or that special manifestation of it, is the aim of the true student of aesthetics.”
—Walter Pater (1839–1894)