Is there a name for the following situation: I have a diagram of categories and functors DO(F) DO(A) ------> DO(B) | | | | H | |H | | v F v A ----------> B It does not commute, nor is there even a 2 cell in either direction. What I do have is illustrated below: DO(A) DO(A) /|\ /|\ / | \ / | \ / | \ / | \ H/ | \DO(F) H/ | \DO(F) / P \ / P' \ / | \ / | \ v | v v | v A <== | ==> DO(B) A ==> | <== DO(B) \ | / \ | / \ | / \ | / F\ | /H F\ | /H \ | / \ | / \ | / \ | / vvv vvv B B and, moreover, P -------> HF | | | | | | | | | | v v FH ------> P' commutes.