72 lines
1.7 KiB
Markdown
72 lines
1.7 KiB
Markdown
# M2 Presentation
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### Introduction slide
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Notes on my internship
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### Plan of the presentation
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First present what is the subject of my study, and what i tried to achieve.
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The whole proof is too formal and complex: Informally prove one specific example.
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Then, i will present the «structure» of the global proof, and show some things discovered along the way
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## GAT and 2-sortification
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### What is a GAT
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### A GAT for a function in set
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A GAT can be composed of three kinds of lines:
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- Sort declarations
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- Objects costructors
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A model is the data of a function from a set to another set i.e. a triple the data of two sets, and a «mapping» between them
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We can spice up this GAT: Gat of isomorphic functions.
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- Equalities
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### A GAT for a category
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Another example of GATs:
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A category is the data of ...... with ...... such that ......
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### A GAT for Type Theory
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Last example that of type theory
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-> a lot to add, contructors, equalities ..., just for the example.
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### 2-sortification
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Known process
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Used by Sestini
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Can simplify a study of GATs to only GATs of two sorts
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### 2-sortification of the Set function GAT
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Sort specification is always the same. O will describe «sorts» and El will describe «objects of that sort»
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Then, we replace Set occuneces by O and we prefix everything else by El
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### 2-sortification of the Type Theoyr GAT
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### Goal of the internship
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## One Example
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### Category of Models & Generalization
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### Category of models of the Transformed GAT
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### Adding transformed sort declarations
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### Constructing the functors
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### Contsructing G3
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### Constructing F3
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### Adjunction FG
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## The complete proof & Discoveries
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### Structure of the proof
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### Fibration of C
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### S from syntax
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## Conclusion
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### Conclusion
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### Future work
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