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For a general theory, one does not need to have $lambda$$\lambda$-directed colimits for any $\lambda$.
The simpliest example is formed by sets and the axiom $(\exists x,y)(x\neq y)$(\exists x,y)(x\neq y)$; idempotents do not split here.
For a general theory, one does not need to have $lambda$-directed colimits for any $\lambda$.
The simpliest example is formed by sets and the axiom $(\exists x,y)(x\neq y); idempotents do not split here.
For a general theory, one does not need to have $\lambda$-directed colimits for any $\lambda$.
The simpliest example is formed by sets and the axiom $(\exists x,y)(x\neq y)$; idempotents do not split here.
For a general theory, one does not need to have $lambda$-directed colimits for any $\lambda$.
The simpliest example is formed by sets and the axiom $(\exists x,y)(x\neq y); idempotents do not split here.
