A category where maps are factorizations - what is this called?

terminology category-theory

Solution 1:

This is called the twisted arrow category. I note with amusement that the linked definition uses exactly the same letters.

Related

Sums of rising factorial powers [duplicate]
The projective model structure on chain complexes
Main Theorems/Techniques for proving Homeomorphism?
(non?)-surjectivity of the exponential map to $SL(2,\mathbb{C})$
Markov chains: is "aperiodic + irreducible" equivalent to "regular"?
What pure mathematics foundations should an applied mathematician have?
Projective closure of an algebraic curve as a compactification of Riemann surface
Finite groups of which the centralizer of each element is normal.
Differentiation of a function $f:\mathbb{Q}\to \mathbb{Q}$(Rational Calculus)
Can we qualitatively predict the strategy of the German and US teams in today's World Cup soccer match?
Question about a basis for a topology vs the topology generated by a basis?
Does the category of locally ringed spaces have products?