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Do compositions of homomorphisms in universal algebra correspond to joins of congruence relations? That is- is the congruence relation $g \circ f(a ) = g \circ f( b) \Leftrightarrow a \sim b $ the join of $f(a ) = f( b) \Leftrightarrow a \sim b $ and $g (c) = g(d) \Leftrightarrow c \sim d $?

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