From b86912b93f02ecfea94c08ada154938fd8bb15e5 Mon Sep 17 00:00:00 2001 From: CDaut Date: Tue, 18 Oct 2022 21:37:48 +0200 Subject: [PATCH] def nat trafo --- chapters/nat_trafo.tex | 29 ++++++++++++++++++++++++++++- main.pdf | Bin 319023 -> 323097 bytes 2 files changed, 28 insertions(+), 1 deletion(-) diff --git a/chapters/nat_trafo.tex b/chapters/nat_trafo.tex index 468ef77..3331eb8 100644 --- a/chapters/nat_trafo.tex +++ b/chapters/nat_trafo.tex @@ -1 +1,28 @@ -\section{Natürliche Transformationen} \ No newline at end of file +\section{Natürliche Transformationen} +\begin{definition}{Natürliche Transformation\\} + Seien + \begin{tikzcd} + \mathscr{C} + \arrow[shift left, "\mathcal{F}"]{r} + \arrow[shift right, "\mathcal{G}"']{r} + & + \mathscr{D} + \end{tikzcd} Funktoren.\\ + Eine natürliche Transformation (nat. Trafo.) $\eta$ von $\mathcal{F}$ nach + $\mathcal{G}$ ist eine Sammlung von Morphismen wie folgt:\\ + $\forall x\in\ob\mathscr{C}$ gilt $\mathcal{F}(x)\xrightarrow{\eta_x}\mathcal{G}(x)$\\ + $x\mapsto\eta_x\in\mor{\mathscr{D}}{\mathcal{F}(x)}{\mathcal{G}(x)}$. Folgendes Diagramm soll also kommutieren:\\ + \begin{figure}[h] + \begin{center} + \begin{tikzcd}[sep=large] + X \arrow[d, "f"'] \\ Y + \end{tikzcd} + \hspace{20mm} + \begin{tikzcd}[sep=large] + \mathcal{F}(x) \arrow[r, "\eta_x"] \arrow[d, "\mathcal{F}(f)"]{}& \mathcal{G}(x) \arrow[d, "\mathcal{G}(f)"]\\ + \mathcal{F}(y) \arrow[r, "\eta_y"] & \mathcal{G}(y) + \end{tikzcd} + \end{center} + \caption{Das kommutative Diagramm für eine natürliche Transformation $\eta$.} + \end{figure} +\end{definition} \ No newline at end of file diff --git a/main.pdf b/main.pdf index 548dd5121a55c282c383d6975f3bb55add43db17..e974e25e010c1d284323f84b7272ff72d763f45e 100644 GIT binary patch delta 74258 zcmZ3#M|kEP;Rylt_Wp+r1de{M>ymz}*k1c@`Z|wXRR;rsjSS6-c}WY^G<<*lvDmay ztMN$5dG-76_ikn_QApS>^#981w9>7iVjhcE&uvNL-*jz-u0>FWtmEZF#?^nm=%2ET zn<)53;JHrTPLng|7fLUeVEcFLj>fZ6+aZijq?kXV+V_@OWg+-?3}H zpY!zS!V_D2AL>uu>7RRCtoGYvsj1thY+k&?>L%BfWhwi=zpr&`O{qEYsq?y0;IotB 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