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```
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{-# OPTIONS --cubical #-}
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{-# OPTIONS #-}
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module MayConcise.Chapter1 where
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open import HottBook.Chapter1
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```
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## 1 What is algebraic topology?
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https://en.wikipedia.org/wiki/Homomorphism
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> A homomorphism is a map between two algebraic structures of the same type (that is of the same name), that preserves the operations of the structures. This means a map f : A → B {\displaystyle f:A\to B} between two sets A {\displaystyle A}, B {\displaystyle B} equipped with the same structure such that, if ⋅ {\displaystyle \cdot } is an operation of the structure (supposed here, for simplification, to be a binary operation), then
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>
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> ```
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> f ( x ⋅ y ) = f ( x ) ⋅ f ( y ) {\displaystyle f(x\cdot y)=f(x)\cdot f(y)}
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> ```
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>
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> for every pair x {\displaystyle x}, y {\displaystyle y} of elements of A {\displaystyle A}.
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```
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```
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## 2 The fundamental group
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```
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homotopy : {X Y : Set} {p q : X → Y}
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π₁ : (X : Set) → (x : X) → Set
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π₁ X x = x ≡ x
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```
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## 3 Dependence on the basepoint
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```
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γ : {X : Set} {x y : X} (a : x ≡ y) → π₁ X x ≡ π₁ X y
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γ a = {! a ∙ ? !}
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```
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## 4 Homotopy invariance
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```
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_⋆
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```
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9
src/MayConcise/Chapter2.lagda.md
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9
src/MayConcise/Chapter2.lagda.md
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```
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{-# OPTIONS #-}
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module MayConcise.Chapter2 where
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```
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## 1 Categories
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```
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```
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