examples/category: elementary pushouts and pullbacks - #2020
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Universal-property definitions of pushout/pullback squares over an arbitrary category, with duality (op_cat), uniqueness up to iso, iso-stability, and transport of pushouts along isos of the apex or span legs.
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examples/category/pushoutScript.sml: elementary (universal-property) definitions of pushout and pullback squares over an arbitrary category, together with their basic theory:is_span_in/is_cospan_in/pushout_square/is_pushout/pullback_square/is_pullbackpushout_pullback_dual— pushout ⇔ pullback in the opposite categorypushout_unique_iso— the pushout object is unique up to isomorphism (iso_objs)pushout_iso_stability— the pushout of an isomorphism is an isomorphismpushout_transport_iso/pushout_transport_dom_iso/pushout_transport_cod_iso/pushout_relabel_span— a pushout is stable under replacing the apex or either span leaf by an isomorphic objectiso_cancel_left—e⁻¹ ∘ (e ∘ x) = xEverything is stated generically over any
is_category cand depends only oncategoryTheory. The existinglimitScripttreats general (co)limits via cones over comma categories but never specializes to pushouts; this file provides the direct elementary formulation.🤖 Generated with Claude Code