diff --git a/Tesi.log b/Tesi.log index 60bfc74..a70c20b 100644 --- a/Tesi.log +++ b/Tesi.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.141592653-2.6-1.40.29 (TeX Live 2026/Arch Linux) (preloaded format=pdflatex 2026.4.6) 19 MAY 2026 15:10 +This is pdfTeX, Version 3.141592653-2.6-1.40.29 (TeX Live 2026/Arch Linux) (preloaded format=pdflatex 2026.4.6) 19 MAY 2026 15:27 entering extended mode restricted \write18 enabled. %&-line parsing enabled. @@ -861,7 +861,7 @@ Package logreq Info: Writing requests to 'Tesi.run.xml'. Here is how much of TeX's memory you used: 26647 strings out of 469515 568827 string characters out of 5470808 - 1335039 words of memory out of 5000000 + 1336039 words of memory out of 5000000 54941 multiletter control sequences out of 15000+600000 640012 words of font info for 86 fonts, out of 8000000 for 9000 14 hyphenation exceptions out of 8191 @@ -885,7 +885,7 @@ exmf-dist/fonts/type1/public/amsfonts/cm/cmsy7.pfb> -Output written on Tesi.pdf (27 pages, 334432 bytes). +Output written on Tesi.pdf (27 pages, 334383 bytes). PDF statistics: 211 PDF objects out of 1000 (max. 8388607) 134 compressed objects within 2 object streams diff --git a/Tesi.pdf b/Tesi.pdf index 7797c18..78e707e 100644 Binary files a/Tesi.pdf and b/Tesi.pdf differ diff --git a/Tesi.synctex.gz b/Tesi.synctex.gz index 766d491..364cad8 100644 Binary files a/Tesi.synctex.gz and b/Tesi.synctex.gz differ diff --git a/Tesi.tex b/Tesi.tex index 945a7b1..a979a01 100644 --- a/Tesi.tex +++ b/Tesi.tex @@ -96,7 +96,7 @@ \begin{theorem}\label{completenesscomma} - Let $\mathcal{A}$ and $\mathcal{B}$ be two finitely cocomplete categories and let $F:\mathcal{A} \to \mathcal{C}$, $\mathcal{B} \to \mathcal{C}$ two functors. If $F$ is a continuous functor - i.e. preserves small colimits - then the comma category $(F\downarrow G)$ is finitely cocomplete; moreover the forgetful functors are continuous. \\ + Let $\mathcal{A}$ and $\mathcal{B}$ be two finitely cocomplete categories and let $F:\mathcal{A} \to \mathcal{C}$, $\mathcal{B} \to \mathcal{C}$ two functors. If $F$ is a cocontinuous functor - i.e. preserves small colimits - then the comma category $(F\downarrow G)$ is finitely cocomplete; moreover the forgetful functors are continuous. \\ Analogously if $\mathcal{A}$ and $\mathcal{B}$ are finitely complete categories and $G: \mathcal{A} \to \mathcal{C}$ is continuos - i.e. preserves small limits - then $(F \downarrow G)$ is finitely complete and both forgetful functors are continuos. \end{theorem}