Pullback of ACSets along a cospan

Given f: B → D and g: C → D, compute the pullback B ×_D C, consisting of pairs (b, c) where f(b) = g(c) for every object type.

Usage

pullback(f, g)

Arguments

f

ACSetTransformation B → D

g

ACSetTransformation C → D

Value

List with pullback, proj1, proj2

Examples

# Pullback of two maps into a common target
D <- path_graph(2) # 1 -> 2
B <- path_graph(2) # 1 -> 2
C <- path_graph(2) # 1 -> 2
f <- ACSetTransformation(list(V = c(1L, 2L), E = 1L), B, D)
g <- ACSetTransformation(list(V = c(1L, 2L), E = 1L), C, D)
pb <- pullback(f, g)
nv(pb$pullback) # 2
#> [1] 2