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1. • CommentRowNumber1.
   • CommentAuthorHarry Gindi
   • CommentTimeJun 2nd 2010
   • (edited Jun 2nd 2010)
   • PermaLink
   Author: Harry Gindi
   Format: MarkdownItexIn Cisinski's [book](http://www-math.univ-paris13.fr/~cisinski/ast.pdf), I'm having trouble understanding what Lemma 1.1.6a is saying, because he refers to the different faces of the cube as lateral, horizontal, horizontal superieur, horizontal inferieur, oblique, etc. Could someone who knows what it's supposed to say, that is, translate the statement of part a.) and the proof (only a paragraph long)? I'd type it out, but the diagram is necessary.

   In Cisinski’s book, I’m having trouble understanding what Lemma 1.1.6a is saying, because he refers to the different faces of the cube as lateral, horizontal, horizontal superieur, horizontal inferieur, oblique, etc.

   Could someone who knows what it’s supposed to say, that is, translate the statement of part a.) and the proof (only a paragraph long)?

   I’d type it out, but the diagram is necessary.

2. • CommentRowNumber2.
   • CommentAuthorDavidRoberts
   • CommentTimeJun 2nd 2010
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexhere's a crack - my French is terrible: Let C be a category admitting inductive limits, and F a class of arrows of C a)If the class F is stable under direct images, for every commutative diagram, blah if the horizontal faces are cocartesian [i.e. pushouts], if the arrow $k:X_1\amalg_{X_0} Y_0 \to Y_1$ is in F, then so is $l:X\amalg_{X_2} Y_2 \to Y$. Proof: We start by forming the following commutative diagram blah The upper horizontal square, (as well as?) the two lateral squares of the cube are cocartesian, and then so is the lower horizontal square. The oblique square is also cocartesian, and then so is the face of the prism (not sure about that last clause) to be continued... Or someone else can do a better job :)

   here’s a crack - my French is terrible:

   Let C be a category admitting inductive limits, and F a class of arrows of C

   a)If the class F is stable under direct images, for every commutative diagram,

   blah

   if the horizontal faces are cocartesian [i.e. pushouts], if the arrow $k:X_1\amalg_{X_0} Y_0 \to Y_1$ is in F, then so is $l:X\amalg_{X_2} Y_2 \to Y$.

   Proof: We start by forming the following commutative diagram

   blah

   The upper horizontal square, (as well as?) the two lateral squares of the cube are cocartesian, and then so is the lower horizontal square. The oblique square is also cocartesian, and then so is the face of the prism (not sure about that last clause)

   to be continued… Or someone else can do a better job :)

3. • CommentRowNumber3.
   • CommentAuthorHarry Gindi
   • CommentTimeJun 2nd 2010
   • (edited Jun 2nd 2010)
   • PermaLink
   Author: Harry Gindi
   Format: MarkdownItexWhich squares are horizontal? The front and back ones, or the front, back, top, and bottom ones? Also, which square is oblique, and which ones are lateral? Edit: Nevermind. I've got it.

   Which squares are horizontal? The front and back ones, or the front, back, top, and bottom ones? Also, which square is oblique, and which ones are lateral?

   Edit: Nevermind. I’ve got it.