Language and Spacetime Description of Meaning 6th Time For KARCEVSKIJ Sergej

 Language and Spacetime

 

 

Description of Meaning

 

6^th Time For KARCEVSKIJ Sergej

 

 

TANAKA Akio

 

 

1 Word consists of meaning and time.

Refer to the following paper.

Structure of Word   Tokyo April 6, 2007

2 Sentence consists of connection of words.

Refer to the following paper.

Generation of Sentence   Tokyo April 13, 2007

3 Now presheaf is presented by MACLANE Saunders.

Presheaf is contravariant functor F on small category C.   F: C^op → Set   (Set is all of small sets and functions.)

Category has duality principle by axiom.

Category C has opposite category C^op.

Arrow f has opposite arrow f ^op.

Object of C^op is object C.

Arrow of C^op 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 Hom_Grp( H,G) makes the relation between H and G clear. ( Hom_Grp( 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

Sekinan Research Field of Language

www.sekinan.org