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| Her 27th gaze was apart from the world… |
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| Her Empty Gaze |
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| 30 relocations and one frotwe. |
Showing posts with label Abstract. Show all posts
Showing posts with label Abstract. Show all posts
Saturday, April 26, 2014
The faces of a computer...
Tuesday, March 18, 2014
And then it happened…
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| And then it happened... |
And then it happened…
Before, kn-though-e-t-w… Though it what, …. light?
flicker; blink.
machine-like piercing/soothing sound…
warm, flappy-flappy, soaring weightless uplifting … MSILE!!!S!@!
flicker; blink.
I was sitting, back.. in my cold seat, un-warmed by another’s recent settling… back on the metro…and it was like it n.e..v…..r…
no strings attached right???
Saturday, December 14, 2013
Sunday, July 28, 2013
Saturday, July 13, 2013
One
sFG364weybsgdhdh!?1!;
Curious? Perfection!!!!
Life clinging body;
Childhood staring adulthood,
Cave blundering lost-kitten;
No walls... blindly suspended (free-fall)-rising.
Starving child..dying, loving reverberation.
Teenage mother gazing, offspring's.
Intersection of worlds;
Two child ended child-umbilical cord.
Self bread-feeding pigeon;
Auto-suckling lactating infant.
Self inducing reflected smile.
Self birthing mother...
Sunday, July 7, 2013
Thursday, May 30, 2013
Wednesday, May 29, 2013
Wednesday, May 8, 2013
Functor Categories as Topoi
Consider the category of functors between two categories $E:=D^C$, with D being Sets. It may be shown that E is complete and co-complete due to the fact Sets is; thinking of each object in E as a map from C to Sets, in the sense of evaluation, it can be shown that $(\varinjlim F_i) (C)= \varinjlim F_i(C)$ where $F_i$ are objects in E. In particular $-\times E: E \rightarrow E$ commultes with both types of limits.
Essentially E inheriting Sets' properties, similarly it can be shown that it is abelian, with enough injective objects (again see See Tamme).
On objects A of E, PE(A) defined to be the set of subfunctors $Hom_E(-,A)xE$ is a functor with values in E, and the subfunctors FxE are in bijection with the morphisms in Nat(F,PE). Hence E is a topos.
The Functor category E as described above is called a presheaf, and in the case of a locally small category, via a Yoneda Embedding it may be though of as enlarging an arbitrary category C in such a way, that the enriched C will be complete, co-complete, abelian and posses enough injectives.
Tuesday, May 7, 2013
A little something on Topoi
A Topos E is a mathematical object called a locally small Category, which has limits and a power object. That is to say that for any object A of E the functor Sub($- \times A$) of objects which factor through $- \times A$ is non-empty member of the category $Sets$. Moreover there is an object of E called the power object of A for which Hom(-,PA)$\cong$ Sub(-,-$\times$ A).
Note: recall since E is locally small Hom(-PA) is a set so the equivalence of objets above is a bijection in Sets.
Some examples of Topoi would be the category sets; here for any object X PX is $\mathscr{P}$(X) its power set. With the natural equivalence of $\phi$: Hom(-,PA)$\cong$ Sub(-,-$\times$ A) to be $\phi$:Hom(1,PB)$\rightarrow$Sub(B).
Note: recall since E is locally small Hom(-PA) is a set so the equivalence of objets above is a bijection in Sets.
Some examples of Topoi would be the category sets; here for any object X PX is $\mathscr{P}$(X) its power set. With the natural equivalence of $\phi$: Hom(-,PA)$\cong$ Sub(-,-$\times$ A) to be $\phi$:Hom(1,PB)$\rightarrow$Sub(B).
Sunday, May 5, 2013
Saturday, March 23, 2013
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