File: HoTT_coq_013.v

package info (click to toggle)
coq 8.20.1%2Bdfsg-1
  • links: PTS, VCS
  • area: main
  • in suites: sid, trixie
  • size: 44,116 kB
  • sloc: ml: 234,160; sh: 4,301; python: 3,270; ansic: 2,644; makefile: 882; lisp: 172; javascript: 63; xml: 24; sed: 2
file content (24 lines) | stat: -rw-r--r-- 880 bytes parent folder | download | duplicates (7)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Set Implicit Arguments.
Generalizable All Variables.

Polymorphic Variant Category (obj : Type) :=.

            Polymorphic Variant Functor objC (C : Category objC) objD (D : Category objD) :=.

            Polymorphic Definition ComposeFunctors objC C objD D objE E (G : @Functor objD D objE E) (F : @Functor objC C objD D) : Functor C E.
Admitted.

Polymorphic Definition ProductCategory objC (C : Category objC) objD (D : Category objD) : @Category (objC * objD)%type.
Admitted.

Polymorphic Definition Cat0 : Category Empty_set.
Admitted.

Set Printing Universes.

Lemma ProductLaw0 objC (C : Category objC) (F : Functor (ProductCategory C Cat0) Cat0) (G : Functor Cat0 (ProductCategory C Cat0)) x y :
  ComposeFunctors F G = x /\
  ComposeFunctors G F = y.
Proof.
  split. (* Error: Refiner was given an argument "(objC * 0)%type" of type "Type" instead of "Set". *)
Abort.