Notation 2.6.1.1.2 (007H): Further Notation for Direct Images

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Table of Contents
Part 1: Sets
Chapter 2: Constructions With Sets
Section 2.6: The Adjoint Triple $f_{*}\dashv f^{-1}\dashv f_{!}$
Subsection 2.6.1: Direct Images
Notation 2.6.1.1.2: Further Notation for Direct Images (cite)

Notation 2.6.1.1.2 ▶ Further Notation for Direct Images

Sometimes one finds the notation

\[ \exists _{f}\colon \mathcal{P}\webleft (X\webright )\to \mathcal{P}\webleft (Y\webright ) \]

for $f_{*}$. This notation comes from the fact that the following statements are equivalent, where $y\in Y$ and $U\in \mathcal{P}\webleft (X\webright )$:

We have $y\in \exists _{f}\webleft (U\webright )$.
There exists some $x\in U$ such that $f\webleft (x\webright )=y$.

We will not make use of this notation in the present work.

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