1 Word consists of meaning and time.
Refer to the following paper.
2 Sentence consists of connection of words.
Refer to the following paper.
3 Now presheaf is presented by MACLANE Saunders.
Presheaf is contravariant functor F on small category C. F: Cop → Set (Set is all of small sets and functions.)
Category has duality principle by axiom.
Category C has opposite category Cop.
Arrow f has opposite arrow f op.
Object of Cop is object C.
Arrow of Cop is arrow f op.
4 Presheaf F gives homomorphism by the following.
V ⊂U ( V and U are arbitrary open sets.)
ρ : F (U) → F (V)
ρ gives restrictive mapping.
5 From category, word is given intuitively as below.
F (V) is starting point of meaning.
F (U) is ending point of meaning.
Presheaf F is time for shifting meaning.
6 Grp that consists of groups and homomorphisms are presented.
Now here exist a group G and other groups H.
Arrow’s set HomGrp( H,G) makes the relation between H and G clear. ( HomGrp( H,G) is all the arrows’ set connecting objects H and G in category Grp.)
Here G is meaning of word. H is elements of meaning G.
7 Meaning of word is clarified by all the arrow’s set.
8 The clarification is called description of meaning.
Tokyo April 16, 2007
No comments:
Post a Comment