One of the things that Jacob Lurie finds important is to "think invariantly": Do not use model dependent definitions. Do not prove model-dependent results.

Here's an example to illustrate what I mean:
"The $\infty$-category of spetra is the free stable $\infty$-category generated by a single object". That's a nice model independent definition of the $\infty$-category of spectra.

One of the things that Jacob Lurie finds important is to "think invariantly": Do not use model dependent definitions. Do not prove model-dependent results.

Here's an example to illustrate what I mean:
"The $\infty$-category of spetra is the free stable $\infty$-category with colimits generated by a single object". That's a nice model independent definition of the $\infty$-category of spectra.

One of the things that Jacob Lurie finds important is to "think invariantly": Do not use model dependent definitions. Do not prove model-dependent results.

Here's an example to illustrate what I mean:
"The oo-category of spetra is the free stable oo-category generated by a single object". That's a nice model independent definition of the oo-category of spectra.

One of the things that Jacob Lurie finds important is to "think invariantly": Do not use model dependent definitions. Do not prove model-dependent results.

Here's an example to illustrate what I mean:
"The $\infty$-category of spetra is the free stable $\infty$-category generated by a single object". That's a nice model independent definition of the $\infty$-category of spectra.