Definition 3.1.2.1.1 (009J): Morphisms of Pointed Sets

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Table of Contents
Part 1: Sets
Chapter 3: Pointed Sets
Section 3.1: Pointed Sets
Subsection 3.1.2: Morphisms of Pointed Sets
Definition 3.1.2.1.1: Morphisms of Pointed Sets (cite)

Statistics Cite

Definition 3.1.2.1.1 ▶ Morphisms of Pointed Sets

A morphism of pointed sets^[1]^[2] is equivalently:

A morphism of $\mathbb {E}_{0}$-monoids in $\webleft (\mathrm{N}_{\bullet }\webleft (\mathsf{Sets}\webright ),\text{pt}\webright )$.
A morphism of pointed objects in $\webleft (\mathsf{Sets},\text{pt}\webright )$.

Footnotes

[1] Further Terminology: Also called a pointed function.

[2] Further Terminology: In the context of monoids with zero as models for $\mathbb {F}_{1}$-algebras, morphisms of pointed sets are also called morphism of $\mathbb {F}_{1}$-modules.

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