$\Box_i\dashv \bigcirc_i$ "$H_th$ is infinitesimal over $H$" $\Box_c\dashv \bigcirc_c$ "$H$ is cohesive over $\infty Grpd$" $(d^*\dashv d_*\dashv i^!)$ "$H_th$ is differential over $H$" such that $(\Box_t\dashv \bigcirc_t)$ "$H_th$ is cohesive over $\infty Grpd$" and $(t_!\dashv t^* \dashv t_*)=(c_!i^*\dashv c^* i_* \dashv c_* i^!)$