Categories of spaces may not be generalized spaces as exemplified by directed graphs
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Logical role, discrete sets, category spaces, thin geometry (es)Descargas
It has long been recognized [G1], [L] that even within geometry (that is, even apart from their algebraic/logical role) toposes come in (at least) two varieties: as spaces (possibly generalized, treated via the category of sheaves of discrete sets), or as categories of spaces (analytic [G2], topological [J], combinatorial, etc.).
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Lawvere, F. W. (1986). Categories of spaces may not be generalized spaces as exemplified by directed graphs. Revista Colombiana De Matemáticas, 20(3-4), 179-186. https://revistas.unal.edu.co/index.php/recolma/article/view/32699
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Derechos de autor 1986 Revista Colombiana de Matemáticas

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