Stability Properties of Pullbacks

Proving that the following morphism properties are stable under pullback (that is the pullback of a morphism with that property must also have that property):
Monic (originally proved in the pullbacks video below), Right-Invertible, Isomorphism, Equalizer.
(This result can also be stated as morphism properties which are preserved by the pullback).

Stating that the pullback of an Epic or Left-Invertible morphisms is not necessarily Epic or Left-Invertible, with the proof to find a counter-example left as an exercise.

CORRECTION: At 14:10 I put that p1 o (p1_R)^(-1) = 1_P, but this should be 1_B, since the domain (and codomain) of that morphism is B, not P.

Video on pullbacks:    • Pullbacks  
Video on Equalizers:    • Equalizers  
Video on Limits:    • Limits & Colimits (via Diagrams, Cone...