Toposes as homotopy groupoids

DOI10.1016/0001-8708(90)90013-DzbMath0783.18004MaRDI QIDQ1813668

Ieke Moerdijk, André Joyal

Publication date: 25 June 1992

Published in: Advances in Mathematics (Search for Journal in Brave)

zbMATH Keywords

cohomologysheavescovering mapGrothendieck toposGrothendieck topologycontinuous groupoid of homotopy classes of paths

Mathematics Subject Classification ID

Topoi (18B25) Abstract and axiomatic homotopy theory in algebraic topology (55U35) Algebraic aspects of posets (06A11) Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) (18F20) Homological algebra in category theory, derived categories and functors (18G99) Grothendieck topologies and Grothendieck topoi (18F10)

Related Items (6)

Extension of topological groupoids and Hurewicz morphisms ⋮ An addendum to “Path-lifting for Grothendieck toposes" ⋮ On the construction of the Grothendieck fundamental group of a topos by paths ⋮ Every étendue comes from a local equivalence relation ⋮ Representing topoi by topological groupoids ⋮ Sheaf Representations and Duality in Logic

Cites Work

• Continuous categories and exponentiable toposes
• An elementary proof of the descent theorem for Grothendieck toposes
• Toposes are Cohomologically Equivalent to Spaces
• An extension of the Galois theory of Grothendieck
• La logique des topos
• The Classifying Topos of a Continuous Groupoid. I
• Connected Locally Connected Toposes are Path-Connected

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