Here's my proposal for higher_algebraic:
1) to move it before exposé 7;
2) add a part on symmetric monoidal model categories (I'll write that);
3) add a brief account on (symmetric) spectra and model structures on them (I'll do that, and maybe Marco will lend me a hand);
4) add a brief account on Lurie's higher algebra: in particular his definition of infinity operad and some comparison with the dendroidal world and with the symmetric model world (Marco will do that, when he has time; in any case, no deadline is scheduled).
Motivations: I'll need a discussion of spectra in exposé XI, but even an expository exposition of them doesn't fit in that chapter. Instead, there I'll do the comparison between k-Module spectra and unbounded chain complexes (which makes sense only after chapter 7 and 8, where the notion of cdga is firstly introduced).
Here's my proposal for higher_algebraic: 1) to move it before exposé 7; 2) add a part on symmetric monoidal model categories (I'll write that); 3) add a brief account on (symmetric) spectra and model structures on them (I'll do that, and maybe Marco will lend me a hand); 4) add a brief account on Lurie's higher algebra: in particular his definition of infinity operad and some comparison with the dendroidal world and with the symmetric model world (Marco will do that, when he has time; in any case, no deadline is scheduled).
Motivations: I'll need a discussion of spectra in exposé XI, but even an expository exposition of them doesn't fit in that chapter. Instead, there I'll do the comparison between k-Module spectra and unbounded chain complexes (which makes sense only after chapter 7 and 8, where the notion of cdga is firstly introduced).