I am trying to understand the tangent $(\infty,1)$ category. It is the fiberwise stabilization of the codomain fibration (which is a functor from the arrow category to the category).
But, intuitively it is clearer to me. The objects of tangent $(\infty,1)$ topos are sheaves of parametrized spectra, bundles of spectra. That is, we associate to each object in the category a spectrum, and to each 1-morphism we associate equivalence between spectra; and homotopies to 2-morphisms, and so on.
Can someone kindly loosen up the first definition a bit accessible to a physics undergrad? I guess it is precisely the second one from the notion of fiberwise stabilisation.
I am interested in tangent $(\infty,1)$ topos as its intrinsic cohomology is twisted cohomology.
