/sci/ - Science & Math

>>9573937
I care little for such petty things.

>>9003997
They just represent source, target, identity and composition. Maybe I should approach this using generic elements. Since I have finite limits in [math]\mathscr{E}[/math], I have a terminal object. Then I would just do stuff like define [math]\tau_x \colon f_0(x)\to g_0(x)[/math], for each such generic element [math]x\colon 1\to C_0[/math]. This would give the ordinary commutative square of natural transformations: for generic elements [math]x, y\colon 1\to C_0[/math], and an internal morphism [math]\varphi\colon x\to y[/math] in [math]C_1[/math], [math]\tau_y \circ f_1(\varphi) = g_1(\varphi)\circ \tau_x[/math].