fd5adb831b
In the previous commit there was still one step missing: that the natural isomorphisms are also unique.
36 lines
1.1 KiB
Text
36 lines
1.1 KiB
Text
/-
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Copyright (c) 2016 Floris van Doorn. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Floris van Doorn
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-/
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import ..groupoid ..functor.basic
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open eq is_trunc iso trunc functor
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namespace category
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definition fundamental_precategory [constructor] (A : Type) : Precategory :=
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precategory.MK A
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(λa a', trunc 0 (a = a'))
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_
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(λa₁ a₂ a₃ q p, tconcat p q)
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(λa, tidp)
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(λa₁ a₂ a₃ a₄ r q p, tassoc p q r)
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(λa₁ a₂, tcon_tidp)
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(λa₁ a₂, tidp_tcon)
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definition fundamental_groupoid [constructor] (A : Type) : Groupoid :=
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groupoid.MK (fundamental_precategory A)
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(λa b p, is_iso.mk (tinverse p) (right_tinv p) (left_tinv p))
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definition fundamental_groupoid_functor [constructor] {A B : Type} (f : A → B) :
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fundamental_groupoid A ⇒ fundamental_groupoid B :=
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functor.mk f (λa a', tap f) (λa, tap_tidp f) (λa₁ a₂ a₃ q p, tap_tcon f p q)
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notation `Π₁` := fundamental_groupoid
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notation `Π₁⇒` := fundamental_groupoid_functor
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end category
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