73 lines
2.6 KiB
TeX
73 lines
2.6 KiB
TeX
\chapter{Planning report}
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I have already implemented multiple essential building blocks for a
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formalization of core-category theory. These concepts include:
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\begin{itemize}
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\item
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Categories
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\item
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Functors
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\item
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Products
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\item
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Exponentials
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\item
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Natural transformations
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\item
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Concrete Categories
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\subitem
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Sets
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\subitem
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Cat
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\subitem
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Functor
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\end{itemize}
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Will all these things already in place it's my assessment that I am ahead of
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schedule at this point.\footnote{I have omitted a lot of other things that
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follow easily from the above, e.g. a cartesian-closed category is simply one
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that has all products and exponentials.}
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Here is a plan for my thesis work organized on a week-by-week basis.
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\begin{center}
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\centering
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\begin{tabular}{@{}lll@{}}
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Goal & Deadline & Risk 1-5 \\ \hline
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Yoneda embedding & Feb 2nd & 3 \\
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Categories with families & Feb 9th & 4 \\
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Presheafs $\Rightarrow$ CwF's & Feb 16th & 2 \\
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Cubical Category & Feb 23rd & 3 \\
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Writing seminar & Mar 2nd & \\
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Kan condition & Mar 9th & 4 \\
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Thesis outline and backlog & Mar 16th & 2 \\
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Half-time report & Mar 23rd & 2 \\
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& Mar 30th & \\
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& Apr 6th & \\
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& Apr 13th & \\
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& Apr 20th & \\
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Thesis draft & Apr 27th & 2 \\
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Writing seminar 2 & May 4th & \\
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Presentation & May 11th & \\
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Attend 1st presentation & May 18th & \\
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Attend 2nd presentation & May 25th & \\
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\end{tabular}
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\end{center}
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The first half part of my thesis-work will be focused on implementing core
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elements of my Agda implementation. These core elements have been highlighted in
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the above table. The elements noted there are the essential bits and pieces I
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need to reach the ambitious goal of getting an implementation of a categorical
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model for Cubical Type Theory. Along the way I will also have formalized
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additional elements of more ``pure'' category theory. I will thus reach my goal
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of formalizing (parts of) category theory.
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The high risk-factors for CwF's and the Kan-condition is due to this being
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somewhat uncharted territory for me at this point.
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It's my plan that I will have formalized the core concepts needed around the
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deadline for the half-time report which is due by March 23rd. Around this point
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I will have a clearer idea of what additional things I need for a model of
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category theory.
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