Utensil's Zettelkasten-style forest of evergreen notes on math and tech.
utensil.tngl.sh/forest/
Minor tweak on limits
+32
-2
+2
-1
trees/tt-002A.tree
+2
-1
trees/tt-002A.tree
+30
-1
trees/tt-004Y.tree
+30
-1
trees/tt-004Y.tree
···
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\table{
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\thead{
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\tr{
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-
\th{Concept}
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+
\th{}
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\th{Limit}
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\th{Colimit}
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}
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}
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\tbody{
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+
% \row{diagram}{\tikzfig{
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% \begin{tikzcd}
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% & \anyobj \\
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% & V \\
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% \bullet && \bullet \\
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% \bullet && \bullet
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% \arrow[dashed, from=1-2, to=2-2]
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% \arrow["{{{{\pi_J}}}}"', from=2-2, to=3-1]
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+
% \arrow["{{{{\pi_{J'}}}}}", from=2-2, to=3-3]
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% \arrow[""{name=0, anchor=center, inner sep=0}, from=3-1, to=3-3]
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% \arrow[""{name=1, anchor=center, inner sep=0}, from=4-1, to=4-3]
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% \arrow["\fD"', shorten <=4pt, shorten >=4pt, Rightarrow, maps to, from=1, to=0]
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% \end{tikzcd}
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% }
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% }{\tikzfig{
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% \begin{tikzcd}
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% & \anyobj \\
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+
% & V \\
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+
% \bullet && \bullet \\
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+
% \bullet && \bullet
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% \arrow[dashed, from=2-2, to=1-2]
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+
% \arrow[from=3-1, to=2-2]
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% \arrow[from=3-3, to=2-2]
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+
% \arrow[""{name=0, anchor=center, inner sep=0}, from=3-3, to=3-1]
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+
% \arrow[""{name=1, anchor=center, inner sep=0}, from=4-3, to=4-1]
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+
% \arrow["\fD"', shorten <=4pt, shorten >=4pt, Rightarrow, maps to, from=1, to=0]
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+
% \end{tikzcd}
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+
% }
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+
% }
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\row{arrows through the vertex}{into the diagram}{out of the diagram}
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\row{on [(co)shape P](tt-000W)}{[pullback](tt-000V)}{[pushout](tt-000X)}
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\row{categories have all ...}{[left exact](tt-002F)}{[right exact](tt-003C)}